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Contact Mathematics  


Room 101
25 University Avenue
West Chester, PA 19383

Phone: 610-436-2440 
Fax: 610-738-0578 
Email: Department Chair

Colloquiums and Seminars

Colloquium and seminar talks will normally be on a Wednesday (usually in UNA 158 from 3:15-4:15), but check the information below for each talk. These seminars/colloquium talks may be by visiting speakers, WCU faculty, or WCU students, and are open to all interested students, faculty and visitors. Send an e-mail to, if you would like to be on the e-mail list to receive advance notice of upcoming talks.

Current Semester



Overview of Phase I, II, and III Clinical Trials

James Godbold, Ph.D

Thursday, January 25, 2018

25 UNA, Room 158


Drug Evaluation Process (Source: Wikipedia)

Drug Evaluation Process (Source: Wikipedia)


Abstract: In this presentation the different phases of clinical trials will be compared and contrasted in terms of the broad clinical objectives of each phase.  Attention will be especially directed to translating the clinical objectives into statistical concepts that will inform the selection of a design at each phase.   A representative design will be used to illustrate each of the three phases, and a phase III design will be illustrated with an example involving treatment for Parkinson’s Disease.


James Godbold, Ph.D., is a biostatistician with experience in medical research and teaching.  He received an M.S. in Statistics from Virginia Tech and a Ph.D. in biostatistics from Johns Hopkins.  He worked at Johnson & Johnson with a group developing ultrasound technology for screening mammography before moving to Memorial Sloan-Kettering where he collaborated with investigators in cancer research.  He spent the last 28 years of his career at the Icahn School of Medicine at Mount Sinai in the Biostatistics Division within the Department of Preventive Medicine, attaining the rank of Research Professor.  In this role, he collaborated with clinical investigators, epidemiologists, and basic scientists throughout the medical school, and he taught biostatistics to medical students and to students in the Master of Public Health program.  In 2015 he retired and moved to Chester County; he now enjoys auditing courses at West Chester University.


Introduction To Category Theory Seminar

First Seminar by Jeremy Brazas, 

Department of Mathematics, West Chester University

Tuesday, January 30th 3:20 - 4:20 pm in UNA 119

 Image for first Category Theory Seminar

Schematic representation of a category with objects X, Y, Z and morphisms f, g, g ∘ f. (The category's three identity morphisms 1X, 1Y and 1Z, if explicitly represented, would appear as three arrows, from the letters X, Y, and Z to themselves, respectively.)

Source - Wikipedia

The content that will be discussed in the seminar will follow the recent textbook "Basic Category Theory" by renowned Category Theorist Tom Leinster. The text is freely available for download on the arXiv (Click here for access to the pdf). 


Seminar Format: The seminar was inspired by graduate student interest so the plan is to have talks/discussions lead by faculty and graduate students on a canonical list of introductory topics. It will be easy to read along with the textbook so one need not know any category theory ahead of time to be a presenter. We will maintain an accessible pace so there is little pressure for presenters. It is perfectly fine if presenters turn the talk into friendly group discussions about things they found issues with. Graduate students are highly encouraged to present.


Computational Science and Applied Mathematics Seminar

Wednesday Jan 31st, 2018,

UNA 155,  3:10 - 4:10 PM

Speaker: Xiaojuan (Cathy) Yu

Title: Model Solute Transport in Streams and Rivers with One-Dimensional Transport with Inflow and Storage (OTIS)


Picture for Xiaojuan (Cathy) Yu's Spring 2018 Seminar


Solute transport in streams and rivers is governed by several differential equations for the hydrologic and geochemical processes. Knowledge of solute fate and transport is needed to aid estimating nutrient uptake in streams, estimating particulate transport, and assessing the fate of contaminants that are released into surface waters. OTIS is a mathematical simulation model used in conjunction with field-scale data to quantify hydrologic processes (advection, dispersion, and transient storage) affecting solute transport and certain chemical reactions (sorption and first-order decay). With given quantities, such as, the mass of the solute and the distance of the reach in the stream, OTIS determines the solute concentrations that result from hydrologic transport and chemical transformation. In this presentation, I demonstrate the application of OTIS with the field data from White Clay Creek and the experimental flumes for my intern experience and current part-time job at Stroud Water Research Center. Our experimental work on the streams and the data analysis using OTIS will help scientists to better understand the solute transport in the local streams and help estimating contamination in the local streams if it happens in the future.

For further information about the Computational Sciences and Applied Mathematics Seminar, e-mail 

Andreas Aristotelous


Chuan Li




 West Chester University
Spring 2018 Mathematics Colloquium


Elizabeth Milićević
Haverford College

“The Rim Hook Rule: Enumerative Geometry via Combinatorics”

Tuesday, February 6, 2018 from 3:20 to 4:15PM
UNA 161

Image for the Elizabeth Milićević Spring 2018 Seminar Talk

The theory of quantum cohomology was initially developed in the early 1990s by physicists working in the field of superstring theory.  Mathematicians then discovered applications to enumerative geometry, counting the number of rational curves of a given degree satisfying certain incidence conditions, but the impact now extends into many other aspects of algebraic geometry, combinatorics, representation theory, number theory, and even back to physics.  In this talk, we will explore the "rim hook rule" which provides a fun and efficient way to compute the quantum cohomology of the Grassmannian of k-dimensional planes in complex n-space.  This talk will be very concrete and completely self-contained, assuming only a background in basic linear algebra.


Elizabeth (Liz) Milićević is an Assistant Professor of Mathematics & Statistics at Haverford College, which is a liberal arts college located just outside Philadelphia. She earned her B.S. in Mathematics from Washington & Lee University, followed by a Ph.D. from the University of Chicago in 2009. Before arriving to Haverford in 2012, Liz did postdoctoral work at the University of Michigan and taught for two years at Williams College. Since her own participation in the programs as a student, Liz has remained actively involved in both the Budapest Semesters in Mathematics (BSM) as an inaugural member of the Advisory Council, as well as the Women and Mathematics (WAM) Program at the Institute for Advanced Study, for which she currently serves on the Program Committee.

Liz's research centers around geometric and topological questions about algebraic varieties such as affine Grassmannians and flag varieties using the methods of algebraic combinatorics, representation theory, and even geometric group theory. Her research program has been supported by an AWM/NSF travel grant, a Simons Collaboration Grant, and a Research at Primarily Undergraduate Institutions (RUI) award from the National Science Foundation (NSF). Liz has also held invited research appointments at the Institute for Computational and Experimental Research in Mathematics (ICERM) and the Max Planck Institute for Mathematics in Bonn, Germany. With support from the Mellon Foundation, Liz co-founded the Mid-Atlantic Algebra, Geometry, and Combinatorics (MAAGC) workshop, an annual series currently funded by the NSF. Liz has also participated as a scientific committee member and co-organizer in many other regional, national, and international conferences, including the weekly Combinatorics, Algebra, and Geometry (CAGE) seminar at the University of Pennsylvania, as well as the annual international workshop on Formal Power Series and Algebraic Combinatorics (FPSAC).


For further information e-mail



Introduction To Category Theory Seminar

Second Seminar by Jeremy Brazas, 

Department of Mathematics, West Chester University

Friday, Febuary 9th 3:00 - 4:00 pm in UNA 158

Category Theory Image from Wikipedia

Schematic representation of a category with objects X, Y, Z and morphisms f, g, g ∘ f. (The category's three identity morphisms 1X, 1Y and 1Z, if explicitly represented, would appear as three arrows, from the letters X, Y, and Z to themselves, respectively.)

Source - Wikipedia

The content that will be discussed in the seminar will follow the recent textbook "Basic Category Theory" by renowned Category Theorist Tom Leinster. The text is freely available for download on the arXiv (Click here for access to the pdf). 


Seminar Format: The seminar was inspired by graduate student interest so the plan is to have talks/discussions lead by faculty and graduate students on a canonical list of introductory topics. It will be easy to read along with the textbook so one need not know any category theory ahead of time to be a presenter. We will maintain an accessible pace so there is little pressure for presenters. It is perfectly fine if presenters turn the talk into friendly group discussions about things they found issues with. Graduate students are highly encouraged to present.


Introduction To Category Theory Seminar

Third Seminar by Jeremy Brazas, 

Department of Mathematics, West Chester University

Tuesday, Febuary 13th 3:20 - 4:20 pm in UNA 119

Category Theory Image

Schematic representation of a category with objects X, Y, Z and morphisms f, g, g ∘ f. (The category's three identity morphisms 1X, 1Y and 1Z, if explicitly represented, would appear as three arrows, from the letters X, Y, and Z to themselves, respectively.)

Source - Wikipedia

The content that will be discussed in the seminar will follow the recent textbook "Basic Category Theory" by renowned Category Theorist Tom Leinster. The text is freely available for download on the arXiv (Click here for access to the pdf). 


Seminar Format: The seminar was inspired by graduate student interest so the plan is to have talks/discussions lead by faculty and graduate students on a canonical list of introductory topics. It will be easy to read along with the textbook so one need not know any category theory ahead of time to be a presenter. We will maintain an accessible pace so there is little pressure for presenters. It is perfectly fine if presenters turn the talk into friendly group discussions about things they found issues with. Graduate students are highly encouraged to present.


Computational Science and Applied Mathematics Seminar

Wednesday February 21st, 2018,

UNA 155,  3:15 - 4:15 PM

Speaker: Dr. Peter Zimmer 

Title: Stochastic Differential Equations: Redux

Flyer Picture for Peter Zimmer's Spring 2018 Seminar Talk

Abstract: Some students, having seen the seminar last fall, asked for more details on the subject, thus we will be REPEATING the same seminar from November 7, 2017 (last fall), with some more examples of computing stochastic ‘derivatives’ and stochastic integrals. Below is a description of last fall’s seminar. In two weeks, March 21, we will have a continuation of this seminar (model various growths processes like stock prices and predator-models).


We will introduce stochastic differential equations, which are ordinary differential equations with a random component. We could use this random component in many manners, one in particular is modeling an error term. So you could think of SDE (stochastic differential equations) as an ode (ordinary differential equation) with a built in error term. This lecture will develop what is called stochastic calculus which will be used to solve some SDEs. We will continue this discussion next spring to include numerical solutions to SDEs with many examples.

For further information about the Computational Sciences and Applied Mathematics Seminar, e-mail 

Andreas Aristotelous 


Chuan Li




West Chester University

Spring 2018 Mathematics Colloquium



Suzanne Dorée
Augsburg University

“Writing Numbers as the Sum of Factorials”

Thursday, March 22, 2018 from 1:45 to 2:45PM
UNA 139

In standard decimal notation, we write each integer as the linear combination of powers of 10.  In binary, we use powers of 2.  What if we used factorials instead of exponentials?  How can we express each integer as the sum of factorials in a minimal way? This talk will explore the factorial representation of integers, including historical connections to permutations, a fast algorithm for conversion, and the secret of the “third proof by mathematical induction.”  Next we’ll extend this representation to rational and then real numbers, ending with some remaining open questions.


Suzanne Dorée is Professor of Mathematics and chair of the Department of Mathematics, Statistics, and Computer Science at Augsburg University in Minneapolis where she has taught since 1989.  She earned her Ph.D. in Character Theory from the University of Wisconsin-Madison. Her research interests include curriculum and materials development and directing undergraduate research in combinatorics. She enjoys teaching mathematics at all levels using pedagogies that support active and inquiry-based learning. Dr. Dorée is active in the Mathematical Association of America, currently serving as Chair of the MAA Congress and Chair of the Council on Programs and Students.  An avid gardener, cook, and designer, she appreciates the importance of getting her hands dirty, and not just in mathematics.


For further information e-mail

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Note: Talks will be added to the schedule throughout the semester. Check back for updates.


Fall 2017

Arthur B. Powell - Rutgers University-Newark  “Challenges and Responses to Prevailing Conceptions of Fractions: Implications for Teaching and Learning”

Wednesday, October 4, 2017 from 3:20 to 4:15PM UNA 155

Powell Talk Picture

A deep understanding of fractions is a gateway to algebra, probability and statistics, the calculus, real analysis, and so on.  Though the Common Core State Standards for Mathematics challenge teachers to teach fractions as points on a number line, prospective teachers and practicing teachers still remain focused on part/whole meanings of fractions.  However, a response to the challenge needs to offer an alternative and prior conception of fractions as numbers before students are able to arrange them on a number line.  Based on cultural historical theory and theoretical and pedagogical of Gattegno (Cuisenaire & Gattegno, 1954; Gattegno, 1970, 1987), I will propose such an alternative, robust conception of fractions and a new instructional model that has been shown to overcome documented shortcomings of a part/whole conception of fractions.  In ending my talk, I will discuss the implication of the alternative conception and new instructional model for the teaching and learning of school mathematics.


Dr. Arthur B. Powell earned his B.S. from Hampshire College in mathematics and statistics, M.A. in mathematics from the University of Michigan, and Ph.D. in mathematics education from Rutgers, the State University of New Jersey. Powell’s primary research interests include the subordination of teaching to learning; mathematics learning through collaboration, discourse, and technology; teacher learning through communities of practice; ethnomathematics; and mathematics for social justice. As a PI on a collaborative, five-year NSF Discovery Research K-12 grant, he has been working with researchers from Drexel University and the Math Forum at the National Council of Teachers of Mathematics to design, implement, and assess the teaching and learning of dynamic geometry through an online collaborative environment, Virtual Mat Teams with GeoGebra His books (co-edited and co-authored) are Math: A Rich Heritage (1995, Globe Fearon); Ethnomathematics: Challenging Eurocentrism in Mathematics Education (1997, SUNY); A Escrita e o Pensamento Matemático: Interações e Potencialidades [Writing and Mathematical Thinking: Interactions and Potentialities] (2006, Papirus); Culturally Responsive Mathematics Education (2009, Routledge); Combinatorics and Reasoning: Representing, Justifying and Building Isomorphisms (2011, Springer); and Métodos de pesquisa em educação matemática—Usando escrita, vídeo e internet [Research methods in Mathematics Education–Using writing, video, and the Internet] (Mercado de Letras, 2015).

For further information e-mail



Paul Zeitz - University of San Francisco “The BS Graph and Other Hidden Images”

Tuesday, October 17, 2017 from 3:20 to 4:15PM UNA 162

Zeitz Talk Image

You have certainly been told that it is good to draw pictures when thinking about math.  We will show several examples that will convince you that visualization is amazingly powerful, both for understanding things as well as for discovering new things that we don't understand.

Paul Zeitz was an undergraduate at Harvard University and he earned his Ph.D. from UC Berkeley in 1992.  After completing his Ph.D. he accepted a teaching position at the University of San Francisco, where he has been ever since.  Before graduate school, Dr. Zeitz taught high school for six years.  Paul is a graduate of Stuyvesant High School in NY and he was a member of the first American IMO team in 1974 and coached several IMO teams in the 1990s, including the "Dream Team" of 1994 which received a perfect score, for the first and only time in history.  He is the co-founder of the SF Math Circle, the Bay Area Mathematical Olympiad, and Proof School.  Dr. Zeitz received MAA’s Haimo Award in 2003.  He wrote The Art and Craft of Problem Solving in 1999 and he has done a 12-hour video series with the same name with The Teaching Company.  Paul’s wife was a national park service ranger so he has had the good fortune of spending many summers and several winters in Yellowstone National Park.

For further information e-mail



Miklós Bóna - University of Florida “An Overview of Pattern Avoiding Permutations: Something Old, Something New”

 Wednesday, October 25, 2017 from 3:20 to 4:15PM UNA 155

Bona Talk Image

We say that a permutation p contains the shorter permutation q as a pattern if p contains |q| entries, not necessarily in consecutive positions, whose pairwise relations to each other are the same as those of the entries of q.  For instance, p = 3576241 contains q = 231, since the first, third and fifth entries of p relate to each other as the entries of q, namely the leftmost entry is the second smallest, the middle one is the largest, and the rightmost entry is the smallest.

In the first part of this talk, we will review the early results of this fascinating and rapidly growing topic, including the celebrated Marcus-Tardos theorem from 2003.  That theorem shows that for any given pattern q, the number of permutations of length n that avoid q is simply exponential, that is, there exists a constant cq so that Sn(q) ≤ cqn.

In the second part, we discuss some more recent developments, such as a sequence of results on the extremely tenacious pattern 1324, a surprising connection to stack-sortable permutations, and the disproof of numerous long-standing conjectures.  Many open problems will also be discussed.


Miklós Bóna completed his undergraduate studies in Budapest and Paris, then obtained his Ph.D. at MIT in 1997 as a student of Richard P. Stanley.  Since 1999, he has taught at the University of Florida, where in 2010 he was inducted to the Academy of Distinguished Teaching Scholars.

Bóna's main fields of research include the combinatorics of permutations, as well as enumerative and analytic combinatorics.  Since 2010, he has been one of the editors-in-chief of the Electronic Journal of Combinatorics.

For further information e-mail



 Peter Zimmer 
Department of Mathematics, West Chester University

Date:  11/01/2017,  Time:  3:15-4:15pm,  Room:  UNA 155

Talk Title:  Stochastic Differential Equations


Picture for Peter Zimmer's seminar talk, Fall 2017


We will introduce stochastic differential equations, which are ordinary differential equations with a random component. We could use this random component in many manners, one in particular is modeling an error term. So you could think of sde (stochastic differential equations) as an ode (ordinary differential equation) with a built in error term. This lecture will develop what is called stochastic calculus which will be used to solve some sdes. We will continue this discussion next spring to include numerical solutions to sdes with many examples.


Eric Stachura
Department of Mathematics, Haverford College

Date:  11/08/2017,  Time:  3:15-4:15pm,  Room:  UNA 155

Talk Title:  Weak Solutions to Refraction Problems in   Metamaterials

Stachura talk image 1Stachura talk image 2Stachura talk image 3


The notion of negative refraction goes back to the work of V. Veselago in the late 1960’s, in which he proposed that light can be bent in such a way that when light strikes a surface, the refracted ray makes a negative angle with the normal. Materials possessing such property do not exist naturally, but have been constructed in the laboratory in the early 2000’s. The research on the behavior of these materials, called metamaterials, has been extremely active in recent years, especially for applications to invisibility cloaking and the development of a “superlens", which can in principle image objects at the smallest scales. In this talk, I will discuss certain refraction problems in the setting of metamaterials. In particular, I will show how to obtain weak solutions (defined analogously to Brenier solutions for the Monge-Ampère equation) to these problems. For one variant of these problems, as in the case of positive refractive indices, a fully nonlinear PDE of Monge-Ampère type arises. Along the way, I will show that surfaces possessing a certain uniform refraction property, in the setting of metamaterials, are in general neither convex nor concave, which greatly contrasts with the case of positive refractive indices. This last result is joint work with Cristian Gutiérrez (Temple).

West Chester University

Fall 2017 Mathematics Colloquium


Shiv Gupta
West Chester University


image for Shiv Gupta's Colloquium Talk

“John H. Conway’s Doomsday Algorithm

(How to Find the Day of the Week for Any Date on the Gregorian Calendar in Five Seconds or Less)”

Wednesday, November 29, 2017 from 3:20 to 4:15PM
UNA 155

In this talk, we shall discuss what is known as John H. Conway’s Doomsday Algorithm for finding the day of the week for any date on the Gregorian calendar.  John H. Conway attributes the idea behind this algorithm to a paper by Lewis Carroll, the author of Alice in Wonderland (published in the March 31, 1887 issue of the journal NATURE).  The only pre-requisite to understand this algorithm is addition and subtraction of natural numbers below 100.  Following this short talk, there will be plenty of time for Q&A and illustration/demonstration of the Doomsday Algorithm.

For further information e-mail



James Mc Laughlin
Department of Mathematics, West Chester University

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Date:  12/06/2017, Time:  3:15-4:15pm, Room:  UNA 155 

Talk Title:  The Mathematics behind Some Modern Public Key Cryptosystems

German Lorenz cipher machine, used in World War II to encrypt very-high-level general staff messages (source: Wikipedia)

German Lorenz cipher machine, used in World War II to encrypt very-high-level general staff messages (source: Wikipedia)

Cryptography could be regarded as “applied number theory”, and modern cryptography is also heavily reliant on computers, so modern cryptography is also highly computational. In this talk the mathematics behind some modern public key cryptosystems are examined (in a public key cryptosystem, the enciphering key is public knowledge, and anyone can encipher and send a message, but only someone with deciphering key can decipher an enciphered message).

This talk will require little mathematics beyond multiplication of integers, and the concept of a remainder when one integer is divided by another.

For further information about the Computational Sciences and Applied Mathematics Seminar, e-mail

Andreas Aristotelous


Chuan Li.


Spring 2017

Shiv Gupta - West Chester University, “Polynomials in Z[x] Which Are Irreducible Over Z But Are Reducible mod p, For Every Prime p"

Wednesday, May 3, 2017 from 3:20 to 4:15PM, UNA 155

Republique Francaise Monetary Note

It is well known that the polynomial x4 + 1 in Z[x] is irreducible over Z but is reducible mod for every prime. We shall discuss this phenomenon and also give a method to create such polynomials and give several examples.

For further information e-mail

Michael Fisher


Shiv Gupta

Stephen F. West- SUNY Geneseo, “Congruence by Superposition – Euclid Made Whole

Wednesday, April 19, 2017 from 3:20 to 4:15PM, UNA 161

Colored Puzzle pieces fitting together

In The Elements, Euclid defined triangle “congruence” using the notion of superposition, but the idea was never formally postulated. In the 1899, in his book, Foundations of Geometry, David Hilbert set forth a modern treatment of triangle congruence by postulating by Side-Angle-Side axiom. In 2010, CCSSM Standards, returning to the notion of superposition, redefined congruence using rigid motions. In this talk we will discuss the questions: (1) Are these notions of triangle congruence equivalent, and (2) what constitutes a “proof” under the CCSSM Standards.

Dr. West is a life-long mathematics educator with degrees from SUNY Oswego, Rutgers University and the University of Texas at Austin. After teaching mathematics in high school for ten years, he moved to SUNY Geneseo where he held a faculty position in the Mathematics Department. During his thirty years at Geneseo he coordinated their highly successful secondary mathematics certification program, served as Chair of Mathematics and was promoted to the rank of Distinguished Teaching Professor of Mathematics.

Throughout his career, Dr. West has contributed to the improvement of mathematics teaching with his professional service. He has been a member of the Association of Mathematics Teachers of NYS for over 40 years, serving as its 38th president and as the editor of the NYS Mathematics Teachers’ Journal. He has served the Mathematical Association of America as the New York State Regional Coordinator of the American High School Mathematics Examination as a member of the Committee on Technology in Math Education and as a Visiting Lecturer. In addition, he has served the National Council of Teachers of Mathematics as both member and chair of the Regional Services Committee.

Dr. West’s teaching and leadership has been recognized with the SUNY Chancellor’s Award for Excellence in Teaching and the MAA Distinguished Teaching Award. In his retirement, Dr. West is a T3 National Instructor and continues to do mathematics, work on his old cars, read avidly and most importantly, watch his ten grandchildren grow!

For further information e-mail

Michael Fisher


Shiv Gupta

Mr. Lane A. D'Alessandro - West Chester University, Optimizing Overall Reproductive Fitness Using Resource Allocation

April 12, 2017, 3:15-4:15 pm, UNA 158

West Chester University Computational Sciences and Applied Mathematics Seminar


Fitness is environment-specific, and many organisms have evolved the ability to alter resource allocation based on perceived environmental cues (e.g., food/mate availability, predation risk). We are developing an optimization model that examines relative resource allocation into growth, reproduction, and defensive morphology under varying conditions. Specifically, we are investigating how reproductive investment in terms of rate and amount changes as a function of predation risk. The survival function utilizes a modified Gompertz-Makeham law for mortality. The fecundity function is the product of the reproductive schedule and output. The reproductive schedule utilizes a gamma distribution and the output is modeled exponentially. Optimizing the fitness model yields the optimal resource allocation and resulting reproductive schedule. This allows us to understand the effects of phenotypic plasticity in life-history traits on the evolution of a post-reproductive period. As predation risk increases, more resources are allocated towards defenses. However, once predation risk is sufficiently high, it becomes more beneficial for the individuals to allocate all their resource towards reproduction.

Mr. Ben Plumridge,Optimizing Overall Reproductive Fitness Using Resource Allocation

Mentor: Dr. Andreas Aristotelous

West Chester University Computational Sciences and Applied Mathematics Seminar


A model is being developed that simulates the dorsal closure process, a stage of drosophila embryogenesis. The apical side of the amnioserosa (a cell monolayer- wound like region on the surface of the embryo) is being represented through polygonal two dimensional representations of cells, with forces acting on their edges and nodes. Those forces are being regulated by the action of actin and myosin. The model is granular enough so various subregions can be studied to the level of the individual cell. Various equations are being tested, describing the evolution of forces generated by the action of the actomyosin network, which itself might be biochemically driven. Eventually, the model may be used to understand mechanisms of dorsal closure that are not easily analyzed in the lab or produce simulation results that might drive new experiments.

Isaac Klapper, Department of Mathematics, Temple University -EXCLUSION AND CLOCK BEHAVIOR IN AN OSCILLATING CHEMOSTAT

April 05, 2017, 3:00-4:00pm, UNA 158

West Chester University Computational Sciences and Applied Mathematics Seminar


Microbes form a large and central part of the global ecosystem. As a consequence of their short reproductive time and their proficiency at exchange of genetic material, it seems plausible that microbes in communities operate at high efficiency (in terms of free energy and nutrient usage) in many contexts. One obvious issue of interest would be the description of species within a microbial community and its dependence on the local environment. Description of niche structure of organisms and how that structure impacts competitiveness has long been a topic of interest among ecologists. Here, in the context of Yellowstone National Park microbial mat, we discuss influence of temporal environment on microbial community species structure. The possibilities of competitive exclusion and clocking behavior are discussed.

Biographical Note:
Professor Isaac Klapper is an expert in fluid dynamics and the mathematical modeling of the various aspects of biofilm formation, evolution and its interactions with its environment. He is the author of numerous publications and the receiver of several grant awards. He received his A.B. in Mathematics from Harvard University in 1986 and his PhD in Applied Mathematics from the Courant Institute, New York University (NYU) in 1991. He was an NSF postdoctoral fellow at the University of Arizona and a visiting assistant professor at UCLA in the Departments of Applied Mathematics. He served as a tenure-track and tenured faculty and rose to the rank of Full Professor at Montana State University where he was also affiliated with the Center of Biofilm Engineering (CBE) at Montana State. In 2012 he moved to Temple University with the appointment of Full Professor, Department of Mathematics with secondary appointment in the Department of Biology.

Ann Trenk, Wellesley College - The World of Graph Theory: Coloring, Scheduling and Solving Mysteries

Monday, March 27, 2017 from 3:20 to 4:15pm, UNA 162


Graph Theory is a field of mathematics that encompasses tools and techniques for modeling and solving real world problems. In this talk, we explore graph coloring and some of its applications and show how graph theory can be useful in problem solving. In one of our problems, six professors are suspects in a library theft. We'll use their testimony together with some graph theory to identify the guilty party. We will also discuss related current research, some of which involves undergraduates. This talk is designed for a general audience.

Ann Trenk is a Professor of Mathematics at Wellesley College where she has taught since 1992. She has published over 30 research articles focused primarily on structured families of graphs and partially ordered sets. Her book, Tolerance Graphs, coauthored with Martin Golumbic, was published by Cambridge University Press in 2004.

In addition to teaching at Wellesley College, Professor Trenk has taught high school students both as a full-time teacher and in summer programs, and more recently has organized math enrichment activities for elementary school children. Professor Trenk was awarded the Wellesley College Pinanski Prize for Excellence in Teaching in 1995.

Lane D'Alessandro and Maggie Celentano - Using Rarefaction to Assess Optimal Sampling Effort in Stream Invertebrates

West Chester University Computational Sciences and Applied Mathematics Seminar

March 22, 2017, 3:15 - 4:15pm, UNA 158

Membership Function Plots

In ecological studies, identifying the number of species present in an ecosystem, also known as identifying the species richness, is key to measuring biodiversity and ecological stability. In order to analyze the species richness of a system, we performed a process known as rarefaction. Through rarefaction, we attempted to identify the number of samples needed to accurately represent a system.

We examined different methods of performing rarefaction, including the combinatorics method and the bootstrap method, and compared them. Both of these methods allowed us to construct a rarefaction curve that plots the number of species as a function of the number of samples taken. Using these rarefaction curves, we then extended the model by examining initial costs and coverages of the samples. These examinations served to identify the number of samples needed to represent the ecosystem. Once we identified the number of samples needed, we compared the results of different months and locations.

As a possible cause of any present differences between months and locations, we examined the number of degree days that occurred over each month. Degree days did not appear to cause any differences between locations.

Ben Plumridge and Cathy Yu - Developing a Habitat Suitability Index for Brown Trout in White Clay Creek Using Fuzzy Logic

West Chester University Computational Sciences and Applied Mathematics Seminar

March 22, 2017, 3:15 - 4:15pm, UNA 158

We are studying which abiotic parameters best explain the presence or absence of brown trout in White Clay Creek and will subsequently use those parameters to develop a Habitat Suitability Index (HSI). The goal of finding an HSI for different habitats is to help researchers improve decision making and increase understanding of species-habitat relationships. Using the dataset provided by Stroud Water Research Center, we are analyzing the correlation or lack thereof between environmental factors and the quantity of brown trout present in that environment. Using fuzzy logic, we are developing a model to determine an HSI, which is a numerical index that represents the capacity of a given habitat to support a selected species.

Klaus Volpert, Villanova University - Financial Derivatives: Engines of the Economy or Weapons of Mass Destruction

March 1, 2017, 3:20 to 4:15pm


Financial Derivatives is the name for a wide variety of products traded in today’s financial markets. Used mostly for risk management, they can also be used for speculation and gambling. They can be both dangerous and beneficial. From a mathematical perspective, the key challenge is to properly evaluate the price and the risk inherent in a derivative contract. In this talk I will give an overview of the three main methods to price derivatives:

  1. The analytic method by Black and Scholes.
  2. The discrete approach by Cox-Ross-Rubinstein, based on binary trees.
  3. Monte-Carlo Methods, which average information obtained from simulating a large number of random walks of the underlying.

Klaus Volpert is associate professor of mathematics at Villanova University. He won the University’s Lindback Award for Excellence in Teaching in 2009 and the EPaDel’s Crawford Award in 2011. Early studies in his native Germany and the 1989 PhD from the University of Oregon were in pure mathematics (algebraic topology), but he has more recently been interested in problems in applied mathematics, specifically at the intersection with finance and economics.Outside of mathematics, he enjoys making music with his family and friends.

Dr. Baoling Ma1,Mathematical Modeling as a Tool for Investigating Lethal and Sub-Lethal Impacts of Environmental Disasters on Sperm Whales

February 22, 2017, 3:00-4:00pm , UNA 158

1Assistant Professor of Mathematics, Department of Mathematics, Millersville University

West Chester University Computational Sciences and Applied Mathematics Seminar


The sperm whale is the largest toothed whale. It is currently on the list of vulnerable species by theInternational Union for the Conservation of Nature and Natural Resources (IUCN). Even though a lot of research has been dedicated to sperm whales, very little is known about their population dynamics. In this talk I will first go over the brief results of our study to investigate the demographic characteristics of the endangered sperm whale population. Our results indicate that these survivorship rates are very delicate, and a slight decrease could result in a declining population, leading to extinction.

The Deepwater Horizon (DWH) oil rig exploded in April of 2010. This environmental disaster has encouraged substantial research efforts to better understand how such disasters affect the resilience of the Gulf of Mexico (GoM) ecosystem. In this talk I will demonstrate how mathematical models can be applied to understand the impacts of such disasters on the dynamics and persistence of marine mammal populations in the Northern GoM under certain assumptions. Matrix population models are developed to study the lethal and sub-lethal impacts. We investigate how reductions in the survival probabilities and in fecundity affect the sperm whale population. We then investigate the long term effect of such an environmental disaster on the population of sperm whales in the GoM. We also inspect the effects of demographic stochasticity on the recovery probabilities and the recovery time of the population.

A.C. Aristotelous1 Diffuse Interface Models and Their Numerical Solution

February 15, 2017, 3:00-4:00pm, UNA 148

1Department of Mathematics, West Chester University


Partial Differential Equation Models based on Cahn-Hilliard type equations will be discussed. Those Models have applications in various fields from material science to biology. Discontinuous Galerkin Finite Element Methods for the solution of Cahn-Hilliard type equations will be presented. For the underline schemes: solvability, energy stability, convergence and error estimates will be established. Simulation results will be provided. Current and future directions will be discussed.

For further information about the Computational Sciences and Applied Mathematics Seminar, e-mail

Andreas Aristotelous


Chuan Li.

Fall 2016

Michelle Cirillo, University of Delaware, Decomposing and Scaffolding the Introduction to Proof

Decomposition of practice can be described as the breaking down of a complex practice into its constituent parts. Mathematical practices, such as proving and mathematical modeling, tend to be complex and in need of productive decompositions. Decompositions are necessary if we are to make progress in teaching important disciplinary practices and sustaining the call to have students’ classroom experiences in each subject more closely resemble their respective disciplines. Through this colloquium, I will provide insights into the work of teachers in practice, specifically some of the conditions, challenges, and issues related to teaching proof at the secondary level. In addition, potential solutions for addressing these challenges will be presented through data and findings from the three-year research project. These findings have implications for teaching reasoning that leads to proof at the middle school level and for teaching proof at the post-secondary level.

Dr. Michelle Cirillo received her PhD from Iowa State University in 2008 after working as a high school mathematics teacher in NY for 8 years. Cirillo’s primary research interests include the teaching of disciplinary practices (e.g., mathematical proof and modeling), classroom discourse, and teachers’ use of curriculum materials. She is especially interested in the space where these three areas intersect. As a co-PI on a five-year NSF Discovery Research K-12 grant, Cirillo has been working with researchers from Michigan State University to design and pilot professional development materials to support secondary mathematics teachers’ facilitation of classroom discourse. In 2010, Cirillo was awarded a research fellowship from the Knowles Science Teaching Foundation to pursue a three-year study on the teaching of proof in high school geometry. She is currently the PI of an NSF-CAREER grant, which builds on the Knowles project. Cirillo was the lead author on the article, Developing curriculum vision and coherence: Adapting curriculum to focus on authentic mathematics, which won a National Council of Teachers of Mathematics Research and Practice Outstanding Publication Award in 2010.

Chuan Li, Department of Mathematics, WCU - Parallel computing of solving Poisson-Boltzmann equation and calculating corresponding electrostatics for large macromolecules and complexes

One common approach to study electrostatics in molecular biology is via numerically solving the Poisson-Boltzmann equation (PBE) and calculating the electrostatic potential and energies. However, all existing numerical methods for solving the PBE become intolerably slow when solving the PBE for large macromolecules and complexes consisting of hundreds of thousands of charged atoms due to high computational cost. Parallel computing is a cutting-edge technique which teams up multiple computing units and significantly speeds up the calculation. In this talk, I will present a set of parallel computing algorithms developed to solve the PBE. As a demonstration of efficiency and capability of these algorithms, computational results obtained by implementing these algorithms in the DelPhi software on live large macromolecules and complexes are given as well.

Chuan Li, Department of Mathematics, WCU - The Extended Parareal Algorithm for Time-and-Space Parallel Computing of the Cable Equation

The Parareal Algorithm introduced by Jacques-Louis Lions, Yvon Maday, and Gabriel Turinici is an efficient method for achieving parallel computing in time direction for solving time-dependent partial differential equations. However, we have not seen in literature a method to effectively incorporate the spatial-parallelized schemes into the framework of the Parareal algorithm in order to obtain both temporal and spatial parallel computing. In this work, we present a work to extend the original Parareal algorithm to effectively embrace spatial-parallelized solvers to accomplish time-and-space parallel computing of the Cable equation on long cardiac tissues.

Spring 2016

Lawrence Washington, University of Maryland -Cannonballs, Donuts, and Secrets: An Introduction to elliptic curvecryptography

Elliptic curves have been around for centuries, but recently they have become very important in cryptography. I’ll start with a light introduction to elliptic curves and then discuss some recent cryptographic applications.

Larry Washington is a professor of Mathematics at the University of Maryland in College Park. He earned his Ph.D. from Princeton University under the supervision of Kenkichi Iwasawa. He has published over 50 research papers and has supervised 25 Ph.D. students. He is the author or coauthor of the following books: Cyclotomic Fields, Elliptic Curves - Number Theory and Cryptography, An Introduction to Number Theory with Cryptography (with James S. Kraft), Introduction to Cryptography with Coding Theory (with Wade Trappe), and Elementary Number Theory (with James S. Kraft).

Heather Russel, University of Richmond - Which graphs are coloring graphs?

For a simple graph G and a positive integer k, the k-coloring graph of G, denoted Ck(G), is the graph whose vertex set is the set of all proper (vertex)k-colorings of G with two k- colorings adjacent if and only if they differ at exactly one vertex of G. In this talk, we consider the question: Which graphs are coloring graphs? We give examples of families of graphs whose members are always, sometimes, and never coloring graphs and discuss techniques useful for investigating this inverse problem. No prior knowledge of graphs is necessary. We will begin with the definition of a graph and give lots of examples along the way! (This is joint work with Julie Beier (Earlham College), Janet Fierson (LaSalle University), Ruth Haas (Smith College), and Kara Shavo (Presbyterian College).)

Dr. Heather M. Russell attended Washington College in Chestertown, MD for her undergraduate work and received degrees in both math and computer science in 2003. She received her Ph.D. in mathematics from The University of Iowa in 2009. She completed two two-year post-doctoral positions at Louisiana State University and University of Southern California before returning to her undergraduate alma mater to teach as an assistant professor for two years. She is now in her second semester as assistant professor at University of Richmond and very much looking forward to breaking the pattern of moving every two years! Her work focuses on knot theory and its connections to graph theory and combinatorial representation theory. She is also very interested in promoting undergraduate research in mathematics and broadening participation in STEM fields. In her spare time, she enjoys running, cooking, traveling, and seeing live music.

Janet Caldwell, Rowan University - Concepts, Skills, and Problem Solving: Ways to Do It All

The demands for raising student achievement ask teachers to “do it all” – teach more math to more students in more depth with more rigor using more technology. Learn about ways to incorporate the development of conceptual understanding, computational and procedural skills, and problem solving to help students learn more. Examples will be drawn from a variety of topic areas in grades 6-12.

Dr. Janet Caldwell received her bachelor’s degree cum laude from Rice University, earning a M.A. and Ph.D. from the University of Pennsylvania. Janet began her career as a secondary mathematics teacher in Texas and Pennsylvania, followed by five years at Research for Better Schools in Philadelphia before coming to Glassboro State College in the fall of 1983. Dr. Caldwell has been an active leader in mathematics education statewide, regionally, and nationally in leadership roles of several different organizations. As the founder and director of the South Jersey Mathematics, Computer, and Science Instructional Improvement Program, Dr. Caldwell has received approximately $11,000,000 in grants to provide professional Statewide Systemic Initiative Regional Center at Rowan; an NSF Math Science Partnership project with Bridgeton, Millville, Vineland, and Toms River; Project SMART with Camden, Gloucester City, and Pennsauken; and the IMPACT project with Millville and Pennsauken. Among many research publications, Dr. Caldwell recently wrote three books for the National Council of Teachers of Mathematics on developing understanding of elementary arithmetic and is an author for Pearson’s elementary mathematics textbooks, enVisionMATH. The Carnegie Foundation selected Dr. Caldwell as the NJ Professor of the Year in 1994 and she received the Distinguished Teaching Award for the NJ Section of the Mathematical Association of America in 2000. She was honored with the Max Sobel Outstanding Mathematics Educator Award in 1994 by the Association of Mathematics Teachers of NJ and by the NJ Association for Supervision and Curriculum Development with the Ernest Boyer Outstanding Educator Award in 2004.Kraft).


Robert Sedgewick, Princeton University - If You Can Specify It, You Can Analyze it - The Lasting Legacy of Philippe Flajolet

The "Flajolet School" of the analysis of algorithms and combinatorial structures is centered on an effective calculus, known as analytic combinatorics, for the development of mathematical models that are sufficiently accurate and precise that they can be validated through scientific experimentation. It is based on the generating function as the central object of study, first as a formal object that can translate a specification into mathematical equations, then as an analytic object whose properties as a function in the complex plane yield the desired quantitative results. Universal laws of sweeping generality can be proven within the framework, and easily applied. Standing on the shoulders of Cauchy, Polya, de Bruijn, Knuth, and many others, Philippe Flajolet and scores of collaborators developed this theory and demonstrated its effectiveness in a broad range of scientific applications. Flajolet's legacy is a vibrant field of research that holds the key not just to understanding the properties of algorithms and data structures, but also to understanding the properties of discrete structures that arise as models in all fields of science. This talk will survey Flajolet's story and its implications for future research.

Robert Sedgewick is the founding chair and the William O. Baker Professor in the Department of Computer Science at Princeton. Prof. Sedgewick's research interests revolve around algorithm design, including mathematical techniques for the analysis of algorithms. He has published widely in these areas and is the author of seventeen books, including a well-known series of textbooks on algorithms that have been best-sellers for decades. Besides "Algorithms, Fourth Edition (with K. Wayne) his other recently published books are “Computer Science: An Interdisciplinary Approach" (with K. Wayne) and "Analytic Combinatorics" (with P. Flajolet). With Kevin Wayne, he is currently actively engaged in developing web content and online courses that have reached over one million people.

Dr. Lin Tan, West Chester University -The Postage Stamp Problem Revisited.

We will take another look at the Postage Stamp Problem in elementary number theory. Instead of the congruence argument, we present a Pickture method, using a graph method so answers to many questions can be seen immediately through the graph. Interesting connections to the cyclotomic polynomials (in abstract algebra) and q-series will be provided, together with the generating function for the problem.

The presentation is totally accessible toundergraduate math students.

Fall 2015

Andreas Aristotelous, West Chester University, Modeling Heterogeneous Biofilms

Free-living biofilms have been subject to considerable attention, and basic physical principles for them are generally accepted. Many host-biofilm systems, however, consist of heterogeneous mixtures of aggregates of microbes intermixed with host material and are much less studied. Here we study models in order to analyze a key property, namely transport limitation and argue a continuous crossover between two regimes is possible:

  1. a homogenizable mixture of biofilm and host that in important ways acts effectively like a homogeneous macro-biofilm and
  1. a relatively sparse distribution of separated micro biofilms within the host matrix with independent local microenvironment.

We will discuss various possible additions/extensions. Numerical solutions for the systems are developed based on a discontinuous Galerkin finite element framework using mesh adaptivity with high order quadratures to accurately resolve fine-scale effects.

Roberta Schoor, Rutgers University Newark - The Complexities Involved in Observing and Understanding Student Engagement

Greater learning is likely to occur when students are meaningfully engaged. However, understanding when and how to view student engagement is not as easy as it may seem. For example, engagement is often characterized along a continuum ranging from disengaged to highly engaged. Such characterizations may be misleading, and in some cases, counterproductive. They do not take into account some of the many different types of engagement that can occur within the context of a lesson. Studies of the affective and cognitive interactions of students in mathematics classrooms have led us to develop the concept of “engagement structures” (Goldin, Epstein, Schorr, Warner, 2011). An engagement structure is a kind of behavioral/affective/social constellation, situated in the person, that becomes active in social contexts. It involves a motivating desire or goal, actions including social behaviors toward fulfilling the desire, supporting beliefs, sequences of emotional states, strategies, and possible outcomes. Importantly, such structures do not feature exclusively ‘‘positive’’ or “negative” emotional feelings, attitudes, beliefs, and/or values. For example, under some conditions, ‘‘negative’’ emotions (like frustration or fear) can contribute to constructive mathematical engagement, and conversely, "positive" feelings (like satisfaction or joy) can detract from such engagement. This talk will focus on how, using the concept of engagement structures, we can begin to understand engagement from an entirely different perspective.

Dr. Roberta Schorr is an Associate Professor in the Department of Urban Education, and a member of the Ph.D. faculty of the Graduate School. Her research focus is on understanding the cognitive and affective components involved in the development of mathematical ideas in students. This research has been funded through several grants totaling over 18 million dollars (funded primarily by the National Science Foundation) where she has served as Principal Investigator or Co-Principal Investigator. She has (co)authored over 80 articles, chapters, and papers, including several commissioned reports, as well a book entitled The Ambiguity of Teaching to the Test.

Ilan Adler, IEOR, UC Berkeley - Optimization, the PPAD complexity class, and bimatrix games

It is well known that many important optimization problems, ranging from linear programming to hard combinatorial problems, can be formulated as linear complementarity problems (LCP). In addition, many engineering and economics problems (such as market equilibrium) can be formulated directly as LCPs.

One particular problem: finding a Nash equilibrium of a bimatrix game (2-NASH) motivated in the mid 1960’s the development of the elegant Lemke algorithm to solve LCPs. While the algorithm always terminates, there is no guarantee that it will process any given problem (that is, find either a solution or a certificate that no solution exists). However, over the years many classes of LCP problems (including 2- NASH) have been shown to be solvable by the algorithm.

Subsequently, early in the 1990’s, Papadimitriou introduced a rich complexity class - PPAD (Polynomial- time Parity Argument on Directed graphs) - composed of problems whose solution is known to exist via a proof based on a certain directed graph which is a generalization of a graph induced by the algorithm. The (relatively) recent discovery that finding a solution to 2-NASH is PPAD-Complete established the very surprising result that every problem in the class of LCPs that are guaranteed to be solved by the Lemke algorithm can be reduced in polynomial time to 2-NASH.

While of great theoretical value, the ingeniously constructed reduction (which is designed for all PPAD problem) is very complicated and difficult to implement. Furthermore, a general benefit of reducing a problem to a matrix game is that the resulting game often provides some insight into the original problem; however, the original reduction makes the resulting games too cumbersome to analyze.

In this talk, I will present a very simple alternative isomorphic reduction from any such LCP to 2-NASH that overcomes these drawbacks, and discuss its implications.

Ilan Adler is a professor in the department of Industrial Engineering and Operations Research at the University of California at Berkeley. Professor Adler holds a B.A in Economics and Statistics from the Hebrew University in Israel, a M.Sc. in Operations Research from the Technion in Israel, and a Ph.D. in Operations Research from Stanford. His research interests are in optimization theory, financial engineering and combinatorial probabilitymodels.

Urban Larsson, Dalhousie University - Absolute Combinatorial Game Theory

This talk concerns a modern approach to disjunctive sum theory in Combinatorial Games. We show that the central idea for the order of short games is maintenance. The classical idea of winning strategy in G-H, via correspondence between outcome classes and order, is too naive (and not correct!). Conway's normal play games are well behaved because of a group structure; in general, the structure is only a partially ordered monoid, and this leads to more difficult problems. We discuss a generalization of normal play, misère play, and scoring play; extending work of Siegel, Ettinger, Renault, and Milley. This is joint work with Nowakowski and Santos.

Urban Larsson received his Ph.D. from Chalmers University of Technology (Sweden) in 2013. He is currently a Killam Postdoctoral Fellow at Dalhousie University in Halifax, Nova Scotia. Prior to pursuing his Ph.D. in mathematics, Dr. Larsson had worked as a journalist, a photographer, a filmmaker, a media teacher, and an electrician.

Spring 2015

John B. Conway, George Washington University - Matrices and Topology

In this talk we consider the set of n by n matrices and ask various topological questions about certain of its subsets. The idea is that to answer such questions we need to use various results from linear algebra. We are thus exposed to a connection between two different areas of mathematics. This talk is accessible to anyone who knows linear algebra and basic convergence results for real numbers and n-dimensional Euclidean space.

John B. Conway was born and raised in New Orleans and went to school there through college, graduating from Loyola University of New Orleans with a degree in Mathematics. Him and his two brothers were the first in his family to graduate from college. He received an NSF Graduate Fellowship, went to Indiana University for one year, then a year at NYU, and two years later he received his PhD from Louisiana State University. (His older brother also earned a PhD in mathematics from Indiana University and was on the faculty of Tulane University before his premature death.) John Conway's first job was at Indiana University where he rose through the ranks before going to the University of Tennessee in 1990 to be the Head of the department. In 2003 Conway accepted a three-year appointment at the National Science Foundation (NSF). After that he became department chair, here at GW, until his retirement in 2011. Almost all of his research lies between analytic function theory and the theory of operators on a Hilbert space. He is attracted by the interaction between these two areas. He has had 19 PhD students and written 10 books as well as many research papers. On the personal side he is married to his high school sweetheart; they met when he was 15 and she was 13. They own a small house in France and since retirement they spend three months a year there. John Conway and his wife have one son who is a professor of history at the Anglo-American School in St Petersburg, Russia. He and his Russian wife have their grandson, Stephen Johnevich.

David Joyner, United States Naval Academy - The Man Who Found God's Number

This is a tale of two problems. For years, Tom Rokicki worked to determine the exact value of God's number for the Rubik's Cube (the smallest number of moves needed to solve the cube in the worst case), a very difficult problem. By the time he solved this, Tom was completely deaf. Digitizing human hearing, and then implementing that into a medical device, is also a very difficult problem. Thanks to recent medical advances, Tom's hearing was restored about the same time that he discovered God's number.

David Joyner received his Ph.D. in mathematics from the University of Maryland, College Park. He held visiting positions at the University of California San Diego, Princeton, and the Institute for Advanced Study before joining the United States Naval Academy in 1987, where he is now a professor. He received the USNA’s Faculty Researcher of the Year award in 2007. His hobbies include writing, chess, photography, and the history of cryptography.

Andreas C. Aristotelous, Temple University- Discontunous Galerkin Finite Elements for Cahn-Hilliard Type Models

A mixed discontinuous Galerkin (DG) finite element method is devised and analyzed for a modified Cahn-Hilliard equation that models phase separation in diblock copolymer melts. The time discretization is based on a convex splitting of the energy of the equation. We prove that our scheme is unconditionally energy stable with respect to a spatially discrete analogue of the continuous free energy of the system, unconditionally uniquely solvable, and convergent in the natural energy norm with optimal rates.

Fully-discrete, discontinuous Galerkin schemes with time dynamic, locally refined meshes in space are developed for a fourth order Cahn-Hilliard equation with an added nonlinear reaction term, a phenomenological model that can describe cancerous tumor growth. The proposed schemes, which are both second-order in time, are based on a primitive variable DG spatial formulation. The schemes are proved to be convergent, with optimal order error bounds, even in the case where the mesh is changing with time.

We also present an efficient nonlinear multigrid solver for advancing our semi-implicit schemes in time.

Numerical tests are presented showing the convergence of the above schemes at the predicted rates and the flexibility of the methods for approximating complex solution dynamics efficiently.

Chuan Li, University of Alabama - Developing Efficient Numerical and Parallel Computing Methods for Solving Parabolic Interface Problems and their Applications in Computational Biophysics

Many computational biophysics applications, such as calculating the electrostatics of molecules/proteins immersed in water phase, simulating heat dissipation in Magnetic Fluid Hyperthermia (MFH) treatment for human cancers, and imitating potential propagation in excitable cardiac tissue, can all be mathematically modeled as the parabolic interface problems. The standard numerical methods for solving partial differential equations (PDEs) often perform poorly for the parabolic interface problems due to the fact that the physical solutions are usually non-smooth or even discontinuous across the arbitrarily-shaped interface of two media. In this talk, I will present my current work towards developing a matched interface and boundary (MIB) method for restoring the accuracy near the interface. The proposed MIB method, when coupled with fully implicit time stepping schemes, such as the operator splitting alternating direction implicit (ADI) and the locally one-dimensional (LOD) schemes, delivers efficient and stable numerical methods for solving parabolic interface problems. Research directions, such as continuous development of the MIB method, implementing the ADI-MIB and LOD-MIB methods for solving the nonlinear Poisson-Boltzmann equation (PBE) in the popular program DelPhi, and performing high performance computing via newly developed parallel algorithms for solving three-dimensional interface problems , will be addressed as well.

Christopher William Wahle - Inferring Gibbs Free Energies of Liquid Mixtures from Noisy Light Scattering Data Using a Nonlinear Partial Differential Equation

Abstract: Experimental determination of mixture free energies is useful in many scientific fields, including biology, material science, and medicine. Free energies can be determined experimentally using a multi-dimensional nonlinear partial differential equation (PDE). The PDE relates the Gibbs free energies of complex liquid mixtures to the degree to which the mixtures scatter light. For a given mixture, light scattering data can be collected experimentally and fed into the PDE, from which the Gibbs free energy can be computed. Errors in light scattering measurements induce errors in computed free energies. Assuming small measurement errors, the PDE is linearized to yield a parabolic PDE which determines the resulting error in free energy.The linearized PDE is used to quantify the errors in free energies inferred from noisy light scattering data.The analysis provides guidelines for efficiently collecting the data needed to compute Gibbs free energies to a desired accuracy. The interesting mathematical aspects of the PDE will be extracted from the complicated physical context from which it arises.

Christopher William Wahle was Assistant Professor at The Rochester Institute of Technology for eight years. He obtained his PhD at Northwestern University, in 2003; his thesis title was “Gas-Solid Nonequilibrium in Filtration Combustion” and his thesis adviser was Bernard J. Matkowsky, Northwestern University.

His current research interests include 1. inferring mixture free energies from light scattering data using a nonlinear PDE 2. statistical thermodynamic modeling of the effects of charge regulation on inter-protein forces 3. combustion and detonation theory.

C Kristopher Garrett - ; A Large Scale Numerical Experiment

In this talk, I will give details on a numerical experiment conducted on one of the largest supercomputers in the world. The experiment involves the comparison of two moment methods for solving a radiation transport equation. One moment method is very fast to compute, but it can exhibit nonphysical behavior such as negative particle densities. The other method is much more expensive to compute, but it ensures positive particle densities which in a coupled code may be essential. The interesting part is when both methods are run at the largest computational scales, the difference in time to solution between the methods diminishes.

But this is only part of the talk. The other part will involve a journey through several mathe- matical subjects required to solve the radiation transport problem. I will touch on computational PDE theory, optimization problems, properties of spherical harmonics, and more.

Sommer Gentry, United States Naval Academy - Optimization, Ethics, and Organs: Mathematical Methods for Ratining Transplantation

The notion of rationing healthcare is taboo: people naturally feel no one should limit the resources spent extending human life, particularly theirs or their loved ones’. Transplantation can transform the lives of organ recipients, but must be rationed by access to the far-too-small supply of donated organs, so it is a microcosm of ethical dilemmas in rationing healthcare. Operations research techniques can maximize the number of life years gained from transplantation, or redistrict geographic allocation units to distribute organs more fairly across large countries like the United States. Paired kidney exchange, in which a living kidney donor who is incompatible with his intended recipient exchanges organs with another incompatible pair, uses graph algorithms for maximum weight matching to select the best combination of exchanges. Beyond the sophistication of methods, the real challenge is to help decision-makers scrutinize how "fair" and "optimal" can be defined. I will share my experiences as a mathematician in the transplant community.

Sommer Gentry is Associate Professor of Mathematics at the United States Naval Academy, and is also on the faculty of the Johns Hopkins University School of Medicine. She is a senior investigator with the Scientific Registry for Transplant Recipients in the U.S. She has a B.S. in Mathematical and Computational Science and an M.S. in Operations Research, both from Stanford University, and a Ph.D. in Electrical Engineering and Computer Science from MIT. She was a Department of Energy Computational Science Graduate Fellow, and won an award for excellence in communicating computational science to a lay audience. She designed matching optimization methods used for nationwide kidney paired donation registries in both the United States and Canada, and is now creating optimized sharing boundaries to help the Organ Procurement and Transplantation Network reduce geographic disparity in liver allocation. Her work has attracted the attention of major media outlets including Time Magazine, Reader’s Digest, Science, the Discovery Channel, and National Public Radio. Gentry has received the MAA’s Henry L. Alder award for distinguished teaching by a beginning mathematics faculty member.

Alex Chen, University of North Carolina - Competing time scales in HIV invasion

Human immunodeficiency virus (HIV) has caused great damage to society in recent decades. One of the reasons for its virulence is the near impossibility of its eradication after an initial infection. Thus, understanding and preventing initial infection is of vital importance. In this talk, we model HIV transmission with partial and stochastic differential equations. We will discuss how an incomplete understanding of the different time scales involved has led to an underestimation of the protective properties of the cervicovaginal mucus (CVM) layer—a diffusional and immunological barrier against HIV—and the implications that this has for vaccine design. In particular, our model suggests that antibodies with high kon (rapid forward reaction rates with virus), rather than low backward reaction rates koff, should provide more effective HIV neutralization. We further demonstrate that mucin proteins within the CVM layer may provide a mechanism to form a “molecular shield” against viral entry. Our models to understand kinetics of neutralization should be broadly applicable to Ab-mediated neutralization of other viral transmissions at mucosal surfaces.

Alex Chen is a Postdoctoral Research Associate at the University of North Carolina, Chapel Hill. Heobtained his PhD at the University of California, Los Angeles, in 2011; his thesis title was “Boundary Tracking in Large Data Sets and Modeling the Evolution of Landscapes” and his thesis adviser was Andrea Bertozzi, University of California Los Angeles.

His current research interests include the following three projects: the modeling and numerical simulation of cell motility, stochastic and deterministic models for mucosal immunity and modeling, the evolution of landscapes through a set of partial differential equations. He also has experience in image processing with application to large data sets.

Fall 2014

Bruce Berndt, University of Illinois at Urbana-Champaign - The Circle and Divisor Problems, Bessel Function Series, and Ramanujan's Lost Notebook

A page in Ramanujan's lost notebook contains two identities for trigonometric sums in terms of doubly infinite series of Bessel functions. One is related to the famous “circle problem” and the other to the equally famous “divisor problem”. We first discuss these classical unsolved problems. Each identity can be interpreted in three distinct ways. We discuss various methods that have been devised to prove the identities under these different interpretations. Weighted divisor sums naturally arise, and new methods for estimating trigonometric sums need to be developed. Trigonometric analogues and extensions of Ramanujan's identities are discussed. The research to be described is joint work with Sun Kim and Alexandru Zaharescu. (The lecture will be entirely expository, except for two short proofs due to Gauss and Dirichlet.)

Bruce Berndt attended college at Albion College, graduating in 1961, where he also ran track. He received his master's and doctoral degrees from the University of Wisconsin–Madison. He lectured for a year at the University of Glasgow and then, in 1967, was appointed an assistant professor at the University of Illinois at Urbana-Champaign, where he has remained since. In 1973–74 he was a visiting scholar at the Institute for Advanced Study in Princeton. He is currently (as of 2006) Michio Suzuki Distinguished Research Professor of Mathematics at the University of Illinois. Berndt is an analytic number theorist who is probably best known for his work explicating the discoveries of Srinivasa Ramanujan. He is a coordinating editor of The Ramanujan Journal and, in 1996, received an expository Steele Prize from the American Mathematical Society for his work editing Ramanujan's Notebooks. In 2012 he became a fellow of the American Mathematical Society. In December 2012 he received an honorary doctorate from SASTRA University in Kumbakonam, India.

Urban Larsson, Dalhousie University - Combinatorial Games and Computability

We study subtraction games on heaps of matches with simple rules, such as: 2 players alternate in removing one or two matches from one heap of say 21 matches until the heap is empty, and the player who cannot move loses. When played on only one heap, these types of games are known to have periodic outcome functions, which means that a computer can solve them. But if we play similar games on several heaps, they become Turing complete, that is, as hard as any mathematical problem. (Partly joint work with Johan Wästlund)

Urban Larsson received his Ph.D. from Chalmers University of Technology (Sweden) in 2013. He is currently a Killam Postdoctoral Fellow at Dalhousie University in Halifax, Nova Scotia. Prior to pursuing his Ph.D. in mathematics, Dr. Larsson had worked as a journalist, a photographer, a filmmaker, a media teacher, and an electrician.

Maciej Wojtkowski, University of Warmia and Mazury, Poland - Markov partitions and 1-dimensional tilings

Bi-partitions are partitions of the 2-dim torus by two parallelograms. They give rise to 2-periodic tilings of the plane, and further to 1-dim tilings which have a host of well known combinatorial properties, e.g. these are Sturmian sequences.
When a bi-partition is a Markov partition for a hyperbolic toral automorphism (= Berg partition), the tilings are substitution tilings. The substitutions preserving Sturmian sequences are known to have the ``3-palindrome property''.
The number of different substitutions was determined by Seebold '98, and the number of nonequivalent Berg partitions by Siemaszko and Wojtkowski '11.
The two formulas coincide. Using tilings we give a simpler proof for the last result. It shows that every combinatorial substitution preserving a Sturmian sequence is realized geometrically as a Berg partition.

Professor Maciej Wojtkowski works in the fields of dynamical systems and differential geometry. He published extensively in mathematics and mathematical physics, and MathNet lists more then 40 papers in his record. He currently holds a position at the University of Warmia and Mazury in Olsztyn, Poland. In the past he was a tenured professor at the University of Arizona, Tucson, AZ. He also visited UC Berkeley (2 years) and ETH in Zurich (1 year). He was invited to give a talk at ICM Beijing in 2002 in the section of Mathematical Physics. He graduated with a PhD from Moscow State University in 1978, under the direction of Professor Vladimir M. Alekseev.

Spring 2014

Aparna Higgins, University of Dayton - Demonic Graphs and Undergraduate Research

Working with undergraduates on mathematical research has been one of the most satisfying aspects of my professional life. This talk will highlight some of the beautiful and interesting research done by my former undergraduate students on line graphs and pebbling on graphs.We will consider line graphs, some pioneering results in pebbling graphs, and pebbling numbers of line graphs. This work has inspired other students to investigate questions in these areas, and it has contributed to my research as well.

Aparna Higgins received a B.Sc. in mathematics from the University of Bombay in 1978 and a Ph.D. in mathematics from the University of Notre Dame in 1983. Her dissertation was in universal algebra, and her current research interests are in graph theory. She hastaught at the University of Dayton, Ohio, since 1984. Although Aparna enjoys teaching the usual collection of undergraduate courses, her most fulfilling experiences as a teacher have come from directing undergraduates in mathematical research. She has advised twelve undergraduate Honors theses, and she has co-directed an NSF-sponsored Research Experiences for Undergraduates program. Aparna is an advocate of academic year undergraduate research at one’s own institution. She has presented workshops (often with Joe Gallian) at mathematics meetings on directing undergraduate research.She enjoys giving talks on mathematics to audiences of various levels and backgrounds. Aparna has been the recipient of four teaching awards -- from the College of Arts and Sciences at the University of Dayton, the Alumni Award (a University-wide award) at the University of Dayton, from the Ohio Section of the Mathematical Association of America, and in 2005, the Deborah and Tepper Haimo Award for Distinguished College or University Teaching, which is the Mathematical Association of America's most prestigious award for teaching. Aparna has served the MAA in many capacities, including being afounding member of, and then chairing, the Committee on Student Chapters, whichhelped create and maintain Student Chapters, provided support to Sections for student activities and provided appropriate programming for undergraduates at nationalmeetings. Aparna is Director of Project NExT (New Experiences in Teaching), a professional development program of the MAA for new or recent Ph.D.s in the mathematical sciences. Project NExT addresses all aspects of an academic career: improving the teaching and learning of mathematics, engaging in research and scholarship, and participating in professional activities. It also provides the participants with a network of peers and mentors as they assume these responsibilities. Aparna has served as President of the Ohio Section, and has served on several committees of the Ohio Section.

Professor Ken Ono, Emory University- Beautiful formulas of Euclid, Rogers and Ramanujan: Fragments of a theory

Abstract: The “golden ratio” is one of the most intriguing constants in mathematics. It has a beautiful description in terms of a continued fraction. In his first letter to G. H. Hardy, Ramanujan hinted at a theory of continued fractions, which greatly expands on this classical observation. He offered shocking evaluations which Hardy described as...

“These formulas defeated me completely...they could only be written down by a mathematician of the highest class. They must be true because no one would have the imagination to invent them”. - G. H. Hardy

Ramanujan had a secret device, two power series identities which were independently discovered previously by Rogers. The two Rogers-Ramanujan identities are now ubiquitous in mathematics.

It turns out that these identities and Ramanujan’s theory of evaluations are hints of a much larger theory. In joint work with Michael Griffin and Ole Warnaar, the author has discovered a rich framework of Rogers-Ramanujan identities, one which comes equipped with a beautiful theory of algebraic numbers. The story blends the theory of Hall-Littlewood polynomials, modular forms, and the representation theory of Kac-Moody affine Lie algebras.

Ken Ono received his BA from the University of Chicago in 1989, and his PhD in 1993 at UCLA where his advisor was Basil Gordon.

Ono's contributions include several monographs and over 140 research and popular articles in number theory, combinatorics, and algebra. He is considered to be an expert in the theory of integer partitions and modular forms. In 2000 he 'greatly' expanded Ramanujan's theory of partition congruences, and in work with Kathrin Bringmann he has made important contributions to the theory of Maass forms, functions which include Ramanujan's mock theta functions as examples. In 2007 Don Zagier gave a Seminar Bourbaki address on the work of Bringmann, Ono, and Zwegers on the mock theta functions. The 2009 SASTRA Ramanujan Prize, awarded to a young mathematician under the age of 32, has been awarded to Kathrin Bringmann for this joint work with Ono. In 2012 Ono made world news for his work proving the last open conjectures contained in Ramanujan's enigmatic death-bed letter to G. H. Hardy.

Ono has received many awards for his research. In April 2000 he received the Presidential Career Award (PECASE) from Bill Clinton in a ceremony at the White House, and in June 2005 he received the National Science Foundation Director's Distinguished Teaching Scholar Award at the National Academy of Science. He has also won a Sloan Fellowship, a Packard Fellowship, and a Guggenheim Fellowship. In 2012 he became a fellow of the American Mathematical Society.

Richard Nowakowski, Dalhousie University - Sum Strategic Solutions

"Last player to move, wins!" games form a nice mathematical structure that allows humans to find good strategies from general principles in complicated situations. We'll look at NIM (and variants as found on Sesame Street) Snort and Maze and discover the best, good, and very, very good (respectively) strategies that should allow a player to win reasonably often.

Richard Nowakowski received his Ph.D. in 1978 from the University of Calgary under the direction of Richard Guy. During his time in Calgary he met John H. Conway and Elwyn Berlekamp whilst they were developing the theory of combinatorial games. After his Ph.D. he obtained a one-year position at Dalhousie University in Halifax, Nova Scotia. Since 1992, he has been a professor of mathematics at Dalhousie University. Dr. Nowakowski has written over 100 research articles on games, pursuit games on graphs, and graphs. Additionally, he has coauthored two books: "Lessons in Play" and "Cops and Robbers". He cites his most valuable lesson learned as “be careful what you call things”.


Hal Switkay, West Chester University - Minimal Solutions to Euler's Six-Squares Problems

We provide an algorithm to generate minimal solutions to Euler’s six-squares problem. The method makes use of the theta series of the square lattice, the two-dimensional integer lattice. We also consider applications to generalizations of Euler’s problem.

This talk should be easily accessible to undergraduates.

Hal M. Switkay grew up in Philadelphia, PA. He earned his B.A. and M.A. in mathematics at the University of Pennsylvania with a minor in philosophy, and his Ph.D. in mathematics at Lehigh University in the study of set theory. After graduation, his interests shifted towards exceptional mathematics, symmetry, lattices, groups, higher-dimensional geometry, voting, statistics, and the sensible communication of abstract information. He has taught mathematics, from remedial to advanced, has done public speaking, is a musician and composer, and has earned certification as a teacher of Tai Chi Easy and as a practitioner of reiki and Thai massage. He has earned a certificate from West Chester University’s graduate program in applied statistics, and is currently enrolled in West Chester University’s graduate certificate program in business. His business card lists the following interests: mathematics; music; philosophy; health and wellness.

Fall 2013

William Dunham, Muhlenberg College - An Afternoon with Euler

Among the greatest of mathematicians is Leonhard Euler (1707-1783), whose insight, industry, and ingenuity are unsurpassed in the long history of mathematics. In this talk, we sketch Euler's life, describe the quantity and quality of his mathematical output, and discuss a few of his more spectacular discoveries.
We then look, in detail, at a specific problem: Euler was challenged to find four different whole numbers, the sum of any pair of which is a perfect square. The numbers he found – namely 18530, 38114, 45986, and 65570 – reveal a remarkable genius in action. We'll follow along to see how he did it and thereby get a sense of why Euler is rightly known as "the Master of Us All."

NOTE: This talk should be of interest to mathematics majors and minors.

William Dunham, who received his B.S. (1969) from the University of Pittsburgh and his M.S. (1970) and Ph.D.(1974) from Ohio State, is the Truman Koehler Professor of Mathematics at Muhlenberg College.

Over the years, Dunham has directed NEH seminars on math history at Ohio State and has spoken on historical topics at the Smithsonian Institution, on NPR's "Talk of the Nation: Science Friday," and at the Swiss Embassy in Washington, DC. In 2008 and again in 2013, he was a Visiting Professor at Harvard University, where he taught a class on the mathematics of Leonhard Euler.

In the 1990s, Dunham wrote three books – Journey Through Genius: The Great Theorems of Mathematics (Wiley, 1990), The Mathematical Universe (Wiley, 1994), and Euler: The Master of Us All (MAA, 1999) – and in the present century he has done two more – The Calculus Gallery: Masterpieces from Newton to Lebesgue (Princeton, 2005) and The Genius of Euler: Reflections on His Life and Work (MAA, 2007). In 2010 he recorded a 24-lecture DVD series for "The Great Courses" on the history of mathematics.

Dunham's expository writing has been recognized by the MAA with the George Pólya Award in 1993, the Trevor Evans Award in 1997 and 2008, the Lester R. Ford Award in 2006, and the Beckenbach Prize in 2008. The Association of American Publishers designated The Mathematical Universe as the Best Mathematics Book of 1994.


Fred S. Roberts, Rutgers University - Defending against H1N1 Virus, Smallpox, and other Naturally Occurring or Deliberately Introduced Diseases: How Can Graph Theory Help?


Our society faces threats from newly emerging diseases such as the H1N1 virus and from diseases such as
smallpox or anthrax that might be introduced by bioterrorists. How can mathematics help us identify the best strategies to prevent the spread of disease and respond to outbreaks? Mathematical modeling of infectious disease goes back to Bernoulli's work on smallpox in 1760 and is widely used today by government agencies such as the Centers for Disease Control and Prevention (CDC) and the Department of Homeland Security. We will explore how simple models based on vertex-edge graphs can be used to explore strategies like vaccination and quarantine.

Fred S. Roberts is a Distinguished Professor of Mathematics at Rutgers University and a member of the graduate faculties in Computer Science, Mathematics, Operations Research, Computational Molecular Biology, BioMaPS (Interdisciplinary Ph.D. Program at the Interface between the Biological, Mathematical, and Physical Sciences), Industrial and Systems Engineering, and Education. He serves as Director of the Command, Control, and Interoperability Center for Advanced Data Analysis (CCICADA), founded in 2009 as a University Center of Excellence (COE) through the US Department of Homeland Security (DHS). Based at Rutgers, CCICADA has 17 partner organizations nationwide and works on such topics as floods and natural disasters, government resource allocation, fisheries regulations law enforcement, container inspection, and large sports venue security. Roberts also served as Director of the Center for Dynamic Data Analysis, the predecessor DHS COE to CCICADA, from 2006 to 2009. For 16 years until 2011, he was Director of DIMACS, the Center for Discrete Mathematics and Theoretical Computer Science, one of the original US National Science Foundation (NSF) Science and Technology Centers, with 15 partner organizations and over 325 affiliated scientists. He is now DIMACS Emeritus Director and Senior Advisor. Roberts is a member of the Board on Mathematical Sciences and Applications, a former member of NSF advisory committees on International Research and Education, Mathematical and Physical Sciences, and Environmental Research and Education, is on the Steering Committee for the World-Wide Program Mathematics of Planet Earth, on the Scientific Advisory Committee to the Institute for Applied Systems Analysis (IIASA), co-chairs the NJ Universities Homeland Security Research Consortium, has served on the Secretary's epidemiology modeling group at the Department of Health and Human Services, and serves on the NJ Governor's Health Emergency Preparedness Advisory Council and the NJ Domestic Security Preparedness Task Force Planning Group.

Roberts is the author of four books, editor of 21 additional books, and author of some 175 scientific articles. His work has been translated into Russian and Chinese and deals with a wide variety of topics, including mathematical models addressing problems of energy modeling, decision making, communication networks, mathematical psychology, measurement, epidemiology, computational biology, sustainability, homeland security, and precollege education. Among his honors and awards, Professor Roberts has been the recipient of a University Research Initiative Award from the Air Force Office of Scientific Research, the Commemorative Medal of the Union of Czech Mathematicians and Physicists, and the Distinguished Service Award of the Association of Computing Machinery Special Interest Group on Algorithms and Computation Theory, and he is a Fellow of the American Mathematical Society. He also received the NSF Science and Technology Centers Pioneer Award in a ceremony at NSF and received an honorary doctorate from the University of Paris-Dauphine.

Spring 2013

Dr. Matthe Beauregard, Job Candidate - Adaptive Splitting Methods in Application to a Quenching-Combustion Model

The development of numerical methods continues to have a tremendous impact on scientific research, in particular, to the study of partial differential equations. Compact methods serve as a fruitful way of increasing the accuracy of a numerical method without increasing the computational cost. As a result, a tremendous amount of focus in the literature has been placed on the study of compact methods and their applications. Still, their application is often done blindly, without proper numerical analysis of the numerical method. Here, the numerical solution of a nonlinear, degenerate reaction-diffusion equation of the quenching type is investigated. An adaptive compact scheme is employed to obtain solutions for the discretized system. The temporal step is determined adaptively through a suitable arc-length monitor function. It is shown that the numerical solution acquired preserves the positivity and monotonicity of the analytical solution. Strong stability is proven in a Von-Neumann sense via the ℓ2-norm. In light of these achievements, subtle restrictions are imposed as a result of implementing the compact scheme, providing a cautionary tale that employing numerical methods without proper analysis is a recipe for divergence, inaccuracy, and inconsistent results.

Students are strongly encouraged to attend as the talk siphons directly from knowledge of calculus, linear algebra, and systems of differential equations.

Matthew Beauregard is a Postdoctoral Associate Professor at Baylor University, Department of Mathematics, Waco, Texas. He obtained his Applied Mathematics, Aerospace and Mechanical Engineering Minor, at the University of Arizona, Tucson, AZ in 2008; his thesis title was "Nonlinear Dynamics of Elastic Filaments Conveying a Fluid and Numerical Applications to the Static Kirchhoff Equations" and his thesis advisors were Dr. Michael Tabor, University of Arizona, and Dr. Alain Goriely, Oxford University. His research develops and analyzes fully adaptive algorithms that attempt to approximate quenching-combustion models, especially near the onset of blow-up, quenching, or the formation of a singularity. The algorithms stem from expertise in the method of lines, operator splitting, Pade approximations, matrix and difference equation theory, and partial differential equation theory.

Mark McKibben (Job Candidate) - Holey Rocks, Indecisive Fluids, Vanishing Beaches & Fiery Neurons: The Unifying Nature of Implicit Stochastic Evolution Equations

Hidden connections often lurk beneath the surface that, once discovered, enable mathematical models of seemingly disparate phenomena to be studied within a single, unified abstract framework. When the models consist of partial differential equations, the form of this structure is an abstract evolution equation.In this talk, we shall begin by illustrating, in a sequence of steps, how an abstract evolution equation can be derived to unify the study of the models alluded to in the title. Then, we will incorporate environmental noise into the models and develop an even more encompassing stochastic theory governing the evolution of these processes. The talk will end with brief commentary on current and future directions of research in this area, including how one accounts for sharp blows to the system, time delays, and “not-so-nice” noise (e.g., fractional Brownian motion).

Mark McKibben is a professor of mathematics in the department of Mathematics and Computer Science at Goucher College in Baltimore, Maryland. He obtained his PhD at Ohio University, in 1999; his thesis title was “Existence Theorems for Nonlinear Functional Differential Equations” and his thesis advisor was Sergiu Aizicovici, Ohio University. His research interests, broadly speaking, is the field of applied functional analysis used to study theoretical issues (e.g., existence/uniqueness, controllability, convergence schemes of various kinds, stability) of abstract deterministic and stochastic evolution equations.

Dr. Matthew Nick J. Moore, Job Candidate - Semi-analytical models for fluids interacting with structures

Reduced models can lend unique insight into physical phenomena by stripping away all but the most essential principles. I will discuss the use of such models in the context of two fluid-structure problems. First, I will discuss motion in viscoelastic fluids. These fluids store and release elastic energy, leading to motion that is characteristically unsteady. A canonical example is the gravitational settling of body, in which terminal velocity is exceeded on a transient timescale. We have recently developed a "weak-coupling" method that gives semi-analytical solutions to this classical problem and other more complicated problems.
I will discuss a biologically-inspired extension in which the body is propelled by an oscillating force, intended to mimic a swimming stroke. Secondly, I will discuss the erosion of bodies by fluid flow. Inspired by natural examples such as the formation of landforms, our study focuses on the mutual interaction between changing shape and flow. Table-top experiments of soft-clay in flowing water reveal the formation of sharp corners and facets, contrary to the common notion that erosion tends to smooth bodies. We appeal to a semi-analytical flow-model that combines an outer flow with a boundary layer flow in order to rationalize these observations and make new predictions.

Matthew "Nick" Moore is an Associate Research Scientist at the Courant Institute of Mathematical Sciences, New York University, New York. He obtained his PhD at University of North Carolina, in 2010; his thesis title was "Stratified flows with vertical layering of density" and his thesis advisors were Richard M. McLaughlin and Roberto Camassa, University of North Carolina. His research interests include Applied and computational mathematics, fluid mechanics especially fluid-structure interactions, complex fluids, evolution equations, nonlinearity, multi-scale problems, stability analysis.

Dr. Ivan Matic (Job Candidate) - Decay and Growth of Randomness

Formation of crystals, spread of infections, and flow of fluids through porous rocks are modeled mathematically as systems consisting of many particles that behave randomly. We will use fluctuations to quantify the randomness, and measure its decay as the number of particles increase.

Then we will study the opposite problem: growth of randomness. It turns out that situations exist where it is beneficial to increase chaos. As one example, we will study methods to anonymously distribute

Ivan Matic is Assistant Research Professor at Duke University, Durham, North Carolina. He obtained his PhD at the University of California, Berkeley, in 2010; his thesis title was "Homogenizations and large deviations" and his thesis advisor was Fraydoun Rezakhanlou. His interests include probability, statistical mechanics, partial differential equations, combinatorics, and dynamical systems. His research focuses are large time behaviors of variational processes related to stochastic Hamilton-Jacobi and Hamilton-Jacobi-Bellman equations (HJ and HJB), random walks in random environments (RWRE), the stochastic Frenkel-Kontorova models (FK), Gibbs measures (GM), and first and last passage percolations (FPP, LPP).

Dr. Tadele Mengesha (Job Candidate) - Mathematical analysis of the Linearized Peridynamic Model

The talk presents a recent work on the mathematical analysis of certain nonlocal models. Our primary example is the peridynamic model of continuum mechanics: a derivative-free, integral-type continuum model that is found to be suitable for modeling materials that naturally form discontinuities such as cracks when deformed. The focus is on the linearized bond-based PD model for isotropic elastic materials. Our analysis is based on some nonlocal Poincare-type inequalities and compactness of the associated nonlocal operators. We also present the basic structural properties of the associated solution space such as compact embedding, separability, completeness and density along with regularity properties of solutions for different types of kernels. Using standard variational techniques we prove the well posedness of the system of equilibrium equations, given as "nonlocal" boundary value problems. Solutions to the nonlocal system are shown to converge to the Navier system of classical elasticity in the event of vanishing nonlocality. Some aspects of the time dependent equations of motion will also be discussed. (This is a joint work with Qiang Du.)

Tadele Mengesha is a Research Associate at Pennsylvania State University. He obtained his PhD at Temple University in 2007; his thesis title was "Sufficient conditions for local minimizers in calculus of variations" and his thesis advisor was Dr. Yury Grabovsky, Temple University. His current research interests include Analysis of partial differential and integral equations, Calculus of Variations. Existence and uniqueness of nonlocal problems and application to peridynamics, regularity of solutions to PDEs with discontinuous coefficients, homogenization of differential and integral operators with oscillatory coefficients, stability of solutions to variational problems.

Dr. Meredith Hegg (Job Candidate) - Automatic Detection and Animation of Weather Fronts

Accustomed as we all are to seeing weather maps depicting warm and cold fronts as well as other meteorological phenomena, it may surprise most people to learn that many of these features do not have universally accepted mathematical definitions. Several different models have been proposed to define warm and cold fronts, but nearly all involve differential operators of order two or higher. When applied to numerical simulation data, approximations of these operators can lead to problems related to noise amplification. As a result, the majority of weather front maps are currently generated manually using heuristic methods. Here we present a new model based on level curves of the norm of the temperature gradient. This model allows us to automatically detect and animate warm and cold fronts and also includes a method for tracing occluded fronts involving the eigenvectors of the Hessian matrix of the temperature function. We'll discuss the basis for this model and compare our results to hand-drawn maps produced by meteorologists.

Meredith Hegg is a Preceptor in Mathematics at Harvard University. She obtained her PhD in Applied Mathematics at Temple University in 2012; her thesis title was "Exact Relations for Elasticity Tensors of Fiber-Reinforced Composites" and her thesis advisor was Dr. Yury Grabovsky, Temple University. Her thesis research was on exact relations in composite materials. Exact relations describe material properties that are maintained during the construction of composites. The theory of exact relations utilizes a non-linear transformation that sends exact relations to subspaces with algebraic properties. Ideas from representation theory are then used to find all exact relations. Her work focuses on elasticity in fiber-reinforced composites. She also has an additional project modeling weather fronts using numerical simulation data.

Lily KhadJavi, Loyola Marymount University - Social Justice and Mathematics: Analyzing Police Practice in Los Angeles

Although racial profiling is not legal, national polls indicate that most Americans believe it is a regular police practice. Beginning in 2002, under the terms of a Consent Decree with the United States Department of Justice, the Los Angeles Police Department collected and publicized general tallies of all traffic stops, the outcomes of those stops, and the race/ethnicity of drivers. Surprisingly, there have been few studies based on this data set.

Originally motivated by the desire to use real-world data and examine social justice issues in introductory statistics courses, this project has resulted in interdisciplinary research in collaboration with a law professor. Through the ACLU, we were able to gain access to disaggregated data from the City of Los Angeles. As in many other parts of the country, we find significant racial and ethnic disparities, for example in search rates. Perhaps most notably, there are significant disparities in the police's use of searches based solely on driver consent, which are less likely to yield discoveries. Since drivers almost universally agree to such searches, we are led to question whether or not legal consent can be understood as an expression of free will. This talk tells the story of this project, including an overview of the data, the social and legal issues raised, and the statistical techniques used, and will be accessible to students and scholars from across disciplines.

Lily Khadjavi received her bachelor's degree from Harvard University and her PhD in Mathematics from the University of California, Berkeley. She is an Associate Professor of Mathematics at Loyola Marymount University in Los Angeles, and this academic year is a Visiting Scholar at the Research and Evaluation Center at John Jay College of Criminal Justice in New York. Her research interests range from algebraic number.

Dr. Kathleen "Katie" Acker (Job Candidate) - Mathhappy: My Research and Me

Mathematics Education as a specialty has allowed me the luxury of choosing a wide variety of topics to research. My published research and my conference presentations reflect this diversity, focusing on themes of education equity, alternative education, history of mathematics and teaching with technology.

While I will review my earlier work, I primarily intend to discuss my experiences using
technology. I also want to think aloud about how to answer the question:

How can emerging technologies be effectively used to enhance all aspects of learning in the mathematics classroom?

Clearly there are previous studies that report upon curricular changes and efficacy of instruction made possible with the inclusion of graphing calculators, spreadsheet programs, and online sources into the mathematics classroom. In my opinion, there are three questions and their implications open to both development and research. They are:

How does the adoption of tablet computers by schools and smart phones by students change instruction delivery and assessment?

What does an ideal e-text for mathematics resemble?

How best could a mathematics classroom be effectively "flipped‟?

Dr. Rachael Brown (Job Candidate) - Community Development in Mathematics Professional Development

This session will share a study considering how a group of middle grades mathematics teachers developed into a community during a 14-week PD experience. The concept of creating a community of practice is a relatively recent idea in education. There is little written, however, about the possibility of a community of practice developing in a short period of time – though the time frame of this PD is consistent with many PD experiences in the United States. In this study, the design of the PD included focus on mathematics content knowledge and active engagement in high cognitive demand tasks with rational number concepts. Both are common recommendations for effective PD. This study found that a community of practice could be developed in this setting. Although no data were collected on the path of the community after the PD, this study provides an example of success of community of practice development within a PD setting with a facilitator intent on not only improving teachers' understanding of rational numbers but attempting to cultivate a community.

Peter Schumer, Middlebury College - Patterns in Pascal's Triangle

In 1653, Blaise Pascal published his "Treatise on the Arithmetical Triangle" which included a description of his eponymous triangle together with some applications to algebra, combinatorics, and probability. Since that time, a great deal more of its structure has been discovered and analyzed. In this talk we will investigate some of the fascinating patterns contained within this arithmetic triangle.

Peter Schumer is the Baldwin Professor of Mathematics and Natural Philosophy at Middlebury College. He earned his B.S. and M.S. from Rensselaer Polytechnic Institute and earned his Ph.D. from University of Maryland, College Park. His areas of interest are elementary and analytic number theory, history of mathematics, and combinatorics. He has written two books, Introduction to Number Theory (PWS) and Mathematical Journeys (Wiley) and many articles in the areas listed above. He is the recipient of The Trevor Evans Award of the MAA for the article, "The Magician of Budapest" that appeared in Math Horizons. His other academic interest is playing and promoting the game of go (have played in 17 U.S. Opens and countless smaller tournaments). He has had sabbaticals at UCSD, Stanford, San Jose State U., Doshisha Univ. in Kyoto, and Keio Univ. in Tokyo. He has taught courses on mathematics and on the game of go in Kyoto, Japan and Shanghai, China.

Marc Chamberland, Grinnell College - The Computer's Role in Mathematical Discovery and Proof

The use of computer packages has brought us to a point where the computer can be used for many tasks: discover new mathematical patterns and relationships, create impressive graphics to expose mathematical structure, falsify conjectures, confirm analytically derived results, and perhaps most impressively for the purist, suggest approaches for formal proofs. This is the thrust of experimental mathematics. This talk will give some examples to discover or prove results concerning geometry, integrals, binomial sums, dynamics and infinite series.

Marc Chamberland obtained his PhD from the University of Waterloo in 1995. He joined Grinnell College in 1997 where he is now the Myra Steele Professor of Natural Sciences and Mathematics. He has published over 40 articles in the areas of differential equations, dynamical systems, and number theory and has spoken about his research in several countries. He is a strong advocate of using computers in mathematical research and has developed an NSF-supported, upper-level, undergraduate course in Experimental Mathematics. Outside of mathematics, he enjoys time with his family (with three children), biking, and meditation.

Irina Svyshch, WCU Master's Student - Thesis Talk

In this thesis we will discuss some basic similarities and differences between real and complex differentiation and line integration. We will show several isomorphic approaches to complex numbers, in particular, the relationship between matrix and complex multiplication. Then, we will discuss significant differences between real and complex differentiation. We will show a non-traditional proof of the theorem on Cauchy-Riemann equations using only the complex linearity of the complex derivative. It turns out that line integration in real and complex cases has many similarities. These similarities will be explored during our discussion. We will finish by showing how the complex variable Cauchy-Goursat Theorem can be proved using the real Green’s Theorem.

Dr. Howard Cohl (Job Candidate) - Fourier and Gegenbauer expansions for a fundamental solution of Laplace's equation on Riemannian spaces of constant curvature

A fundamental solution of Laplace's equation is derived on Riemannian spaces of constant curvature, namely in hyperspherical geometry and in the hyperboloid model of hyperbolic geometry. These fundamental solutions are given in terms of finite-summation expressions, Gauss hypergeometric function, definite integrals and associated Legendre functions with argument given in terms of the geodesic distance on these manifolds. Fourier and Gegenbauer expansions of these fundamental solutions are derived and discussed.

Carl Pomerance, Dartmouth College - Sums and Products

What could be simpler than to study sums and products of integers? Well maybe it is not so simple since there is a major unsolved problem: For arbitrarily large numbers N, is there a set of N positive integers where the number of pairwise sums is at most N1.99 and likewise, the number of pairwise products is at most N1.99? Erdös and Szemerédi conjecture no. This talk is directed at another problem concerning sums and products, namely how dense can a set of positive integers be if it contains none of its pairwise sums and products? For example, take the numbers that are 2 or 3 more than a multiple of 5, a set with density 2/5. Can you do better? This talk reports on recent joint work with P. Kurlberg and J. C. Lagarias.

Carl Pomerance received his B.A. from Brown University in 1966 and his Ph.D. from Harvard University in 1972 under the direction of John Tate. During the period 1972—99 he was a professor at the University of Georgia, with visiting positions at the University of Illinois at Urbana-Champaign, the University of Limoges, Bell Communications Research, and the Institute for Advanced Study. In the period 1999—2003 he was a Member of the Technical Staff at Bell Laboratories. Currently he is the John G. Kemeny Parents Professor of Mathematics at Dartmouth College and Research Professor Emeritus at the University of Georgia.
A number theorist, Pomerance specializes in analytic, combinatorial, and computational number theory, with applications in the field of cryptology. He considers the late Paul Erdös as his greatest influence.

Pomerance was an invited speaker at the 1994 International Congress of Mathematicians, the Mathematical Association of America (MAA) Pólya Lecturer for 1993--95, and the MAA Hedrick Lecturer in 1999. More recently he was the Rademacher Lecturer at the University of Pennsylvania in 2010. He has won the Chauvenet Prize (1985), the Haimo Award for Distinguished Teaching (1997), and the Conant Prize (2001).

He is a Fellow of the American Association for the Advancement of Science (AAAS) and of the American Mathematical Society. He is the president of the Number Theory Foundation, a past vice president of the MAA and past chair of the Mathematics Section of the AAAS. He is the author of nearly 200 published papers and one book.

Hal Switkay(West Chester University ) - Visualizing 24 Dimensions, Listening to Groups

We continue to discuss the sensible communication of abstract information. Examples will be drawn from among the following topics: the graphical and cartographic display of data; the geometry of the 24-dimensional Leech lattice; melodies associated with finite groups.

Hal M. Switkay grew up in Philadelphia, PA. He earned his B.A. and M.A. in mathematics at the University of Pennsylvania with a minor in philosophy, and his Ph.D. in mathematics at Lehigh University in the study of set theory. After graduation, his interests shifted towards exceptional mathematics, symmetry, lattices, groups, higher-dimensional geometry, voting, statistics, and the sensible communication of abstract information. He has taught mathematics, from remedial to advanced, has done public speaking, is a musician and composer, and has earned certification as a teacher of Tai Chi Easy™ and as a practitioner of reiki and Thai massage. He has earned a certificate from West Chester University’s graduate program in applied statistics, and is currently enrolled in West Chester University’s graduate certificate program in business. His business card lists the following interests: mathematics; music; philosophy; health and wellness.

Ms. Kim Johnson (Job Candidate) - The proportional reasoning of pre-service teachers at the beginning of their teacher preparation program

The purpose of this study is to examine the proportional reasoning of pre-service teachers at the beginning of their teacher preparation program using a developmental shifts model described by Lobato and Ellis (2010). The analysis of the data suggests that the shifts model is hierarchical for those participants who have either made all four shifts in their proportional reasoning or who provide evidence of only completing the first shift. The remaining participants provide evidence that they are in the process of making shifts 2, 3, and 4. For these participants the model does not appear to remain hierarchical. This is based upon the inconsistent evidence they provide while completing proportional reasoning problems. The findings in this study provide teacher educators with knowledge about the nature of the development of pre-service teachers' proportional reasoning. In particular, this study highlights four misconceptions: reasoning quantitatively, recognizing ratios as measurement, misconceptions about ratios and fractions, and the obstacle of linearity. Transformative learning theory (Mezirow, 1991) explains how pre-service teachers can overcome these misconceptions. This theory requires a disorienting dilemma in order to help individuals engage in rational discourse and critical reflection about previous assumptions. This study on proportional reasoning illustrates how four problems were able to provide pre-service teachers with a disorienting dilemma causing them to engage in rational discourse with the researcher and critically reflect on their previous assumptions in order to transform their proportional reasoning. The knowledge gained from this research can be used to develop courses to transform the understanding that pre-service teachers have of ratio and proportion. This ultimately will enhance the proportional reasoning opportunities they provide their students in their future classrooms.

Professor Sergei Sergeev (University of Birmingham, UK) - Tropical convexity over max-min semirings

We develop an analogue of convex geometry over the max-min semiring, starting with description of segments, hyperplanes and semispaces, and some separation and non-separation results. We derive the max-min analogues of Caratheodory, Radon and Helly theorems, and give some colorful extensions.

Dimension of max-min convex sets will be also introduced and discussed.

This talk is based on joint work with Prof. Viorel Nitica.

Fall 2012

Professor Mike Fisher (West Chester University Mathematics Department)

  • Combinatorial Games Theory Seminar - I
  • Combinatorial Games Theory Seminar - II
  • Combinatorial Games Theory Seminar - III
  • Combinatorial Games Theory Seminar - IV
  • Combinatorial Games Theory Seminar - VI
  • Combinatorial Games Theory Seminar - VII
  • Combinatorial Games Theory Seminar - VIII
  • Combinatorial Games Theory Seminar - IX

Alex Rice (Bucknell University) - Arithmetic Patterns in Dense Sets of Integers

Arithmetic Combinatorics is a rapidly developing area with close connections to number theory, combinatorics, harmonic analysis and ergodic theory. Roughly speaking, the field is concerned with finding and counting arithmetic structures in sets, often contained in the integers, and it includes such seminal results as Szemeredi's Theorem on arithmetic progressions and the Green-Tao Theorem on arithmetic progressions in the primes. Here we give a brief introduction and survey of some foundational results in this area, and later we focus on improvements and generalizations of two theorems of Sarkozy, the qualitative versions of which state that any set of natural numbers of positive upper density necessarily contains two distinct elements which differ by a perfect square, as well as two elements that differ by one less than a prime number. Included will be joint work with Neil Lyall and Mariah Hamel.

Alex Rice is a Visiting Assistant Professor in the Department of Mathematics at Bucknell University in Lewisburg, PA. He received his Ph. D. in mathematics from the University of Georgia, and his current research interests are in arithmetic combinatorics.

Jimmy Mc Laughlin (West Chester University)


Professor Viorel Nitica(West Chester University Mathematics Department) - A Coloring Invariant for Ribbon L-Tetrominos

In this talk we investigate several tiling problems for regions in a square lattice by ribbon L- shaped tetrominoes. One of our results shows that tiling of the first quadrant by ribbon L-tetrominoes is possible only if it reduces to a tiling of the first quadrant by 2x4 and 4x2 rectangles. A consequence of the result is the classification of all rectangles that can be tiled by ribbon L-shaped tetrominoes.

Garth Isaak (Lehigh University) - Perfect Maps

Arranging 00011101 on a circle, the consecutive triples are exactly the 8 distinct binary triples. Can we do something similar with a larger alphabet and longer strings? These are called DeBruijn cycles and have a long and interesting history. More recently higher dimensional versions called perfect maps have been investigated. Try, for example creating a 9 by 9 array with entries 0,1,2 such that when wrapped on a torus each of the 81 distinct 2 by 2 patterns with 3 symbols appears exactly once. Mathematical and algorithmic questions and applications related to both of these will be presented.

Garth Isaak received an undergraduate degree with majors in Chemistry, Mathematical Sciences and Physics from Bethel College in Kansas, a Ph.D. from RUTCOR, the Operations Research Center at Rutgers University. Following two postdoctoral years at Dartmouth he moved to Lehigh University where he now Professor of Mathematics and Associate Dean for Research and Graduate Studies in the College of Arts and Sciences.

Professor Rosemary Sullivan (West Chester University) - A Modification of Sylvester's Four Point Problem

In 1865, Sylvester posed the problem of finding the probability that four points randomly chosen with a uniform distribution over a compact convex region K in the plane form the vertices of a convex quadrilateral. This led to substantial research on the ratio
rho_K = E(area(T))/area(K) ,
where T denotes a triangle formed by three independent and uniformly distributed points in K. In this talk we consider the problem of studying the behavior of the ratio
rho_P* = E(area(T))/E(L^2) ,
where L is the distance between two independent points with distribution P and T is a triangle with three independent vertices with distribution P. We call this the Modified Sylvester Four Point Problem.


Professor Whitney George(West Chester University) - An Introduction to Knot Theory

One of the underlying goals in knot theory is to determine when two knots are equivalent. A knot is simply an embedded circle in space. Therefore, we can try to answer this question with hands-on examples. However, this simple task can become difficult and the need for mathematics becomes relevant. In this talk, we will discuss some basic knot invariants, such as crossing number, and the three Reidemeister move, and then extending them to links.

Spring 2012

JGengxin Li (Yale University) - The Improved SNP Calling Algorithms for Illumina BeadArray Data

Genotype calling from high throughput platforms such as Illumina and Affymetrix is a critical step in data processing, so that accurate information on genetic variants can be obtained for phenotype-genotype association studies. A number of algorithms have been developed to infer genotypes from data generated through the Illumina BeadStation platform, including GenCall, GenoSNP, Illuminus, and CRLMM. Most of these algorithms are built on population-based statistical models to genotype every SNP in turn, such as GenCall with the GenTrain clustering algorithm, and require a large reference population to perform well. These approaches may not work well for rare variants where only a small proportion of the individuals carry the variant. A fundamentally different approach, implemented in GenoSNP, adopts a SNP-based model to infer genotypes of all the SNPs in one individual, making it an appealing alternative to call rare variants. However, compared to the population-based strategies, more SNPs in GenoSNP may fail the Hardy-Weinberg Equilibrium test. To take advantage of both strategies, we propose the two-stage SNP calling procedures, to improve call accuracy for both common and rare variants. The effectiveness of our approach is demonstrated through applications to genotype calling on a set of HapMap samples used for quality control purpose in a large case-control study of cocaine dependence. The increase in power with our proposed method is greater for rare variants than for common variants depending on the model.

Gengxin Li is currently a Postdoctoral Associate in the Division of Biostatistics, Department of Epidemiology and Public Health at Yale University. She received a dual-major Ph.D. degree in Statistics and Quantitative Biology at Michigan State University. Her current research interests are high-dimensional data analysis, Bayesian method, Dirichlet process, longitudinal data analysis, Statistical genomics, Statistical genetics, Bioinformatics and Clinical Trials.

Meredith Hegg (Temple University) - Exact Relations for Fiber-Reinforced Elastic Composites

Predicting the effective elastic properties of a composite material based on the elastic properties of its constituent materials is extremely difficult, even when the microstructure of the composite is known. However, there are special cases where certain properties in constituents always carry over to the composite, regardless of microstructure. We call such instances exact relations. The general theory of exact relations allows us to find all of these relations in a wide variety of contexts including elasticity, conductivity, and piezoelectricity. We combine this theory with certain results from representation theory to find all exact relations in the context of elasticity of fiber-reinforced polycrystalline composites and thereby generate new information about this widely-used class of materials.

Meredith Hegg is currently a PhD student in the Department of Mathematics at Temple University. Her main area of research is currently Mechanics of Deformable Solids, and she expects to obtain her PhD in May 2012. Her thesis adviser is Dr. Yury Grabovsky.

John H. Conway (Princeton University) - The First Field

We all know one field that contains 0,1,2,..., but, logically, there is an earlier field that is defined as follows. We first fill in the addition table, subject to the condition that before we fill in the entry for a+b, we must have already filled in all entries a'+b and a+b' with a'<a and b'<b. Then, the entry at a+b is to be the least possible number that is consistent with the result's being a part of the addition table of a field.

We then tackle the multiplication table of a field with the given addition. Again, the entries are to be the least possible one's subject to this requirement; this construction produces a very strange field in which 8 is a fifth root of unity. Amazingly, this field actually has practical applications.

John H. Conway is a prolific mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He has also contributed to many branches of recreational mathematics, notably the invention of the cellular automaton called the Game of Life.

Conway is currently Professor of Mathematics and John Von Neumann Professor in Applied and Computational Mathematics at Princeton University. He studied at Cambridge, where he started research under Harold Davenport. He received the Berwick Prize (1971), was elected a Fellow of the Royal Society (1981), was the first recipient of the Pólya Prize (LMS) (1987), won the Nemmers Prize in Mathematics (1998), and received the Leroy P. Steele Prize for Mathematical Exposition (2000) of the American Mathematical Society.

Andrew Crossett (Carnegie Mellon University) - Refining Genetically-Inferred Relationships Using Treelet Smoothing

Heritability, or fraction of the total trait variance attributable to additive genetic effects, is an important concept in quantitative genetics. Originally, heritability was only measurable by examining groups of very closely related individuals, such as twin studies. More recently, methods have been proposed to analyze population samples containing only distantly related individuals using a random effects model. To do so they estimate the relatedness of all pairs of individuals in the population sample using a dense set of common genetic variants, such as SNPs, and evaluate their relationships to subject trait values. We build on their approach, focusing on improved estimates of pairwise familial relationships. We propose a new method for denoising genetically inferred relationship matrices, and refer to this general regularization approach of positive semi-definite matrices as Treelet Covariance Smoothing. On both simulated and real data, we show that better estimates of the relatedness amongst individuals lead to better estimates of the heritability.

Jeffrey Beyerl (Clemson University) - On the Factorization of Eigenforms

Modular forms fall within the realm of complex analysis and number theory, with notable applications in theoretical physics. Hecke operators act on spaces of modular forms, and spectral theory implies the existence of eigenforms. My recent research, which will be presented at this talk, has investigated the factorizations of these eigenforms. This type of investigation is relatively new, having started in 1999 when Eknath Ghate and William Duke independently discovered that the product of two eigenforms is again an eigenform only when it is trivially so.

Jeffrey Beyerl is a graduate student in the Department of Mathematics at Clemson University. His main area of research is presently in the field of modular forms, and he expects to obtain his PhD in May 2012. His thesis advisers are Kevin James and Hui Xue.


Tieming Ji (Iowa State University) - Borrowing Information across Genes and Experiments for Improved Error Variance Estimation in Microarray Data Analysis

Statistical inference for microarray experiments usually involves the estimation of error variance for each gene. Because the sample size available for each gene is often low, the usual unbiased estimator of the error variance can be unreliable. Shrinkage methods, including empirical Bayes approaches that borrow information across genes to produce more stable estimates, have been developed in recent years. Because the same microarray platform is often used for at least several experiments to study similar biological systems, there is an opportunity to improve variance estimation further by borrowing information not only across genes but also across experiments. We propose a lognormal model for error variances that involves random gene effects and random experiment effects. Based on the model, we develop an empirical Bayes estimator of the error variance for each combination of gene and experiment and call this estimator BAGE because information is Borrowed Across Genes and Experiments. A permutation strategy is used to make inference about the differential expression status of each gene. Simulation studies with data generated from different probability models and real microarray data show that our method outperforms existing approaches.

Whitney George (University of Georgia) - Twist Knots and the Uniform Thickness Property

In 2007, Etnyre and Honda defined a new knot invariant called the Uniform Thickness Property in order to better understand Legendrian knots. The classification of Legendrian knots in R^3 with the standard contact structure has been a slow process in comparison to the topological classification in R^3. In this talk, we will discuss what makes Legendrian knots more delicate than topological knots, and how the Uniform Thickness Property can help in their classification. My current research investigates the Uniform Thickness Property with respect to positive twist knots which we will discuss towards in the second half of this talk.

Whitney George is a graduate student in the Department of Mathematics at the University of Georgia. Her main area of research is presently in contact topology, and is focused towards knots and surfaces in R^3 with the standard contact structure, and she expects to obtain her PhD in May 2012. Her thesis adviser is Gordana Matic.

Andrew Parrish (Illinois at Urbana-Champaign) - Pointwise Convergence of Averages of L1 Functions on Sparse Sets.

Joint work with P. LaVictoire (University of Wisconsin, Madison) and J. Rosenblatt (UIUC).

The behavior of time averages when taken along subsets of the integers is a central question in subsequence ergodic theory. The existence of transference principles enables us to talk about the convergence of averaging operators in a universal sense; we say that a sequence {an}; is universally pointwise good for L1, for example, if the sequence of averages 1/NΣ_{n=0};^{N-1};f ° LT^{-an};(x) converges a.e. for any f ∈ L1 for every aperiodic measure preserving system (X; B; T; ). Only a few methods of constructing a sparse sequence that is universally pointwise L1-good are known. We will discuss how one can construct families of sets in Zd which are analogues of these sequences,
as well as some challenges and advantages presented by these higher-dimensional averages.

Andrew Parrish is a visiting Assistant Professor in the Department of Mathematics at the University of Illinois at Urbana-Champaign. His current research interests are in ergodic theory, particularly subsequence ergodic theory, with applications to additive combinatorics and harmonic analysis. He obtained his PhD in May 2009 at the University of Memphis. His thesis adviser was Mate Wierdl.

Alissa Crans (Loyola Marymount University) - A Fine Prime

In celebration of your mathematical achievements on this special day we will investigate fun facts related to Leap Days! We'll discuss mathematicians associated to this day and various calendar systems. In addition, we will explore the numerous interesting properties of the number 29. Of course it's prime, but in fact, it's a twin prime, Sophie Germain prime, Lucas prime, Pell prime, and Eisenstein prime. It's also a Markov number, Perrin number, tetranacci number and Stormer number! We'll see all of this, and more, as we congratulate the newest members of Pi Mu Epsilon for their wonderful accomplishments.

Alissa S. Crans earned her B.S. in mathematics from the University of Redlands in 1999 and her Ph.D. in mathematics from the University of California at Riverside in 2004, under the guidance of John Baez. She is currently an Associate Professor of mathematics at Loyola Marymount University and has held positions at Pomona College, The Ohio State University, and the University of Chicago.
Alissa's research is in the field of higher-dimensional algebra and her current work, funded by an NSA Young Investigator Grant, involves categorifying algebraic structures called quandles with the goal of defining new knot and knotted surface invariants. She is also interested in the connections between mathematics and music, and enjoys playing the clarinet with the Santa Monica College wind ensemble.
Alissa is extremely active in helping students increase their appreciation and enthusiasm for mathematics through coorganizing the Pacific Coast Undergraduate Mathematics Conference together with Naiomi Cameron and Kendra Killpatrick, and her mentoring of young women in the Summer Mathematics Program (SMP) at Carleton College, the EDGE program, the Summer Program for Women in Mathematics at George Washington University, the Southern California Women in Mathematics Symposium, and the Career Mentoring Workshop. In addition, Alissa was an invited speaker at the MAA Spring Sectional Meeting of the So Cal/Nevada Section and the keynote speaker at the University of Oklahoma Math Day and the UCSD Undergraduate Math Day. She is a recipient of the 2011 Merten M. Hasse Prize for expository writing and the Henry L. Alder Award for distinguished teaching.

Stefaan Delcroix (California State University, Fresno) - A Generalization of Bertrand's Postulate

Bertrand's Postulate states that for any n > 1, there is at least one prime between n and 2n. We will give an elementary proof of the following generalization: Let k be a fixed number. Then for all n ≥ max{4000, 162k^2}, there are at least k primes between n and 2n.

Stefaan Delcroix (California State University, Fresno) - Locally Finite Simple Groups

A group $G$ is locally finite if every finite subset of $G$ generates a finite subgroup. In this talk, we study infinite, locally finite, simple groups (=LFS-groups). We will introduce some standard definitions and properties, divide the LFS-groups into three categories and provide examples of each category. Next, we study a specific category (LFS-groups of $p$-type) into more detail. This allows us to show some local characterization of each category. Time permitting, we discuss a general construction of LFS-groups of $p$-type.

Born and raised in Belgium, Stefaan finished his masters in mathematics at the University of Ghent (in Belgium). He spent the next three years working on his Ph.D. at Michigan State University under the guidance of Prof. Ulrich Meierfrankenfeld. The subject of his thesis was locally finite simple groups of p-type and alternating type. In June 2000, Stefaan finished his Ph.D. at the University of Ghent. For two years, he worked as a Visiting Assistant Professor at the University of Wyoming in Laramie. Since 2002, Stefaan has worked at California State University, Fresno.

Shiv Gupta (West Chester University) - On Euler's Proof of Fermat's Last Theorem For Exponent Three

We shall discuss some aspects of Euler's proof of Fermat's Last Theorem for exponent three. This talk will be suitable for students who have taken (or currently taking) a course on Theory of Numbers (Mat 414/514).

Jimmy Mc Laughlin (West Chester University) - Hybrid Proofs of the q-Binomial Theorem and other q-series Identities. I

The proof of a q-series identity, whether a series-to-series identity such as the second iterate of Heine’s transformation, a basic hypergeometric summation formula such as the q-Binomial Theorem or one of the Rogers-Ramanujan identities, generally falls into one of two broad camps.

In the one camp, there are a variety of analytic methods.

In the other camp there are a variety of combinatorial or bijective proofs, the simplest of course being conjugation of the Ferrer’s diagram for a partition.

In this series of talks we use a “hybrid” method to prove a number of basic hypergeometric identities. The proofs are “hybrid” in the sense that we use partition arguments to prove a restricted version of the theorem, and then use analytic methods (in the form of the Identity Theorem) to prove the full version.

Jimmy Mc Laughlin (West Chester University)

  • Hybrid Proofs of the q-Binomial Theorem and other q-series Identities. II
  • Hybrid Proofs of the q-Binomial Theorem and other q-series Identities. III
  • Some Partition Bijections in Igor Pak's "PARTITION BIJECTIONS, A SURVEY

Sergei Sergeev (University of Birmingham, UK.) - Tropical convex geometry and two-sided systems of tropical inequalities

Tropical mathematics emerged in 1960's as a linear encoding of some problems in discrete optimization and scheduling. In a nutshell, it studies "spaces" over the max-plus algebra, which is the set of real numbers where taking maximum plays the role of addition, and addition plays the role of multiplication. In the tropical mathematics, negative infinity plays the role of zero, hence any real number is "positive" in the tropical sense. Hence, there are connections with nonnegative linear algebra (in particular, Perron- Frobenius theory), and convex geometry. To this end, tropical spaces can be viewed as an analogue of convex cones, and many results of convex analysis have their tropical analogues, which will be reviewed. Tropical linear two-sided systems Ax = Bx, where matrix-vector multiplication is defined using the tropical arithmetics, are the algebraic encoding of tropical convex cones. Geometrically, such systems represent the tropical convex cones as intersection of tropical halfspaces. Methods for finding a solution to such two-sided systems stem from combinatorial game theory, more specifically, from the theory of deterministic mean-payoff games. We will also touch upon some problems like the tropical linear programming that can be viewed as parametric extension of two-sided systems, and give rise to parametric extensions of mean-payoff games.

Hal Switkay (West Chester University) - The Sensible Communication of Abstract Information

We consider the engagement of the senses in the process of communicating and learning the abstractions of mathematics. Examples are provided from the history of mathematics continuing through current developments, including Markov processes, analytic geometry, statistics, decision theory, 24-dimensional geometry, and the musical representation of groups.

This talk should be easily accessible to undergraduates.

Hal M. Switkay earned his Ph.D. in mathematics at Lehigh University in the study of set theory. After graduation, his interests shifted towards symmetry, lattices, groups, and higher-dimensional geometry. He has taught mathematics, from remedial to advanced, has done public speaking, is a musician and composer, and has earned certification as a teacher of Tai Chi Easy and as a practitioner of reiki and Thai massage. He is currently enrolled in West Chester Universitys graduate certificate program in applied statistics. His business card lists the following interests: mathematics; music; philosophy; health and wellness; and syncretic

Keith Devlin (Stanford University) - Leonardo Fibonacci and Steve Jobs

The first personal computing revolution took place not in Silicon Valley in the 1980s but in Pisa in the 13th Century. The medieval counterpart to Steve Jobs was a young Italian called Leonardo, better known today by the nickname Fibonacci. Thanks to a recently discovered manuscript in a library in Florence, the story of how this little known genius came to launch the modern commercial world can now be told.

Based on Devlin’s latest book The Man of Numbers: Fibonacci’s Arithmetical Revolution (Walker & Co, July 2011) and his co-published companion e-book Leonardo and Steve: The Young Genius Who Beat Apple to Market by 800 Years.

Keith Devlin is a mathematician at Stanford University in California. He is a co-founder and Executive Director of the university's H-STAR institute, a co-founder of the Stanford Media X research network, and a Senior Researcher at CSLI. He has written 31 books and over 80 published research articles. His books have been awarded the Pythagoras Prize and the Peano Prize, and his writing has earned him the Carl Sagan Award, and the Joint Policy Board for Mathematics Communications Award. In 2003, he was recognized by the California State Assembly for his "innovative work and longtime service in the field of mathematics and its relation to logic and linguistics." He is "the Math Guy" on National Public Radio.

He is a World Economic Forum Fellow and a Fellow of the American Association for the Advancement of Science. His current research is focused on the use of different media to teach and communicate mathematics to diverse audiences. He also works on the design of information/reasoning systems for intelligence analysis. Other research interests include: theory of information, models of reasoning, applications of mathematical techniques in the study of communication, and mathematical cognition. He writes a monthly column for the Mathematical Association of America, "Devlin's Angle”.

Elwyn BerleKamp (University of California, Berkley) - Combinatorial Games: Hackenbush and Go

This talk will review the rudiments of combinatorial game theory [1] as exemplified by a game called Hackenbush. Positions are seen to have values, which are sums of numbers and infinitesimals, such that the winner depends on how the total value compares with zero.

We then discuss how refinements of this theory have been applied to the classical Asian board game called Go. The most important tool is the "cooling operator" [2], which maps combinatorial games into other combinatorial games. In the first application, many late stage Go endgame positions [3] are shown to be combinatorial games which, when cooled by 1, often reduce to familiar numbers and infinitesimals. Combinatorial game theory then enables its practitioner to win the endgame by one point. In the second application, Nakamura[4] has shown that liberties can also be viewed as combinatorial games which become familiar numbers and infinitesimals when cooled by 2. In a large class of interesting positions, this approach identifies the move(s), if any, which win the capturing race.

Although not prerequisite to this talk, more details can be found in these references:

[1] Berlekamp, Conway, and Guy: Winning Ways, Chap 1

[2] Berlekamp, Conway, and Guy: Winning Ways, Chap 6

[3] Berlekamp and Wolfe: Mathematical Go

[4] Nakamura, in Games of No Chance, vol 3

Elwyn Berlekamp was an undergraduate at MIT; while there, he was a Putnam Fellow (1961). Professor Berlekamp completed his bachelor's and master's degrees in electrical engineering in 1962. Continuing his studies at MIT, he finished his Ph.D. in electrical engineering in 1964; his advisors were Claude Shannon, Robert G. Gallager, Peter Elias and John Wozencraft. Berlekamp taught at the University of California, Berkeley from 1964 until 1966, when he became a researcher at Bell Labs. In 1971, Berlekamp returned to Berkeley where, as of 2010, he is a Professor of the Graduate School.

He is a member of the National Academy of Engineering (1977) and the National Academy of Sciences (1999). He was elected a Fellow of the American Academy of Arts and Sciences in 1996. He received in 1991 the IEEE Richard W. Hamming Medal, and in 1998 the Golden Jubilee Award for Technological Innovation from the IEEE Information Theory Society.

Berlekamp is one of the inventors of the Welch-Berlekamp and Berlekamp-Massey algorithms, which are used to implementReed-Solomon error correction. In the mid-1980s, he was president of Cyclotomics, Inc., a corporation that developed error-correcting code technology. With John Horton Conway and Richard K. Guy, he co-authored Winning Ways for your Mathematical Plays, leading to his recognition as one of the founders of combinatorial game theory. He has studied various games, including Fox and Geese and other fox games, dots and boxes, and, especially, Go. With David Wolfe, Berlekamp co-authored the book Mathematical Go, which describes methods for analyzing certain classes of Go endgames.

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