Each Thursday there will be a mathematics seminar (usually in UNA 125 from 3:15-4:15), while
colloquium talks will normally be on a Wednesday (usually in UNA 158 from 3:15-4:15).
These seminars/colloquium talks may be by visiting speakers, WCU faculty, or WCU students,
and are open to all interested students and faculty.
Send an e-mail to jmclaughl@wcupa.edu,
if you would like to be on the e-mail list to receive advance notice of upcoming talks.
Previous Semesters: Fall 2008,
Spring 2008,
Fall 2007,
Spring 2007,
Fall 2006,
Summer 2006,
Spring 2006,
Thursday, January 22nd, 2009
3:15 - 4:15 pm in UNA 125
Professor Lin Tan (West Chester University)
WHAT IS THE OMEGA PROCESS AFTER ALL?, Part II
We will show the essence of Macmahon's
Omega Process in his Combinatorial Analysis in an entirely elementary
fashion, inspired by results from Diophantine equations and Diophantine
inequalities, for $\Omega_=$ and $\Omega_{\geq}$ respectively, by Gordan (an
invariant theorist) and Dickson (a number theorist), among others. We will use
Macmahon's list, Jimmy's triangle problem and some example from Andrews, Paule and Reise as our launching pad to illustrate the idea, in particular what the
denominators and numerators in the corresponding generating functions account
for.
Thursday, January 29th, 2009
3:15 - 4:15 pm in UNA 125
Professor Lin Tan (West Chester University)
WHAT IS THE OMEGA PROCESS AFTER ALL?, Part III
We will show the essence of Macmahon's
Omega Process in his Combinatorial Analysis in an entirely elementary
fashion, inspired by results from Diophantine equations and Diophantine
inequalities, for $\Omega_=$ and $\Omega_{\geq}$ respectively, by Gordan (an
invariant theorist) and Dickson (a number theorist), among others. We will use
Macmahon's list, Jimmy's triangle problem and some example from Andrews, Paule and Reise
as our launching pad to illustrate the idea, in particular what the
denominators and numerators in the corresponding generating functions account
for.
Wednsday, February 4th, 2009
3:20 - 4:10 pm in UNA 158
Professor Viorel Nitica (West Chester University)
RIGIDITY OF ABELIAN COCYCLES
We will define the cohomology of a
dynamical systems and will summarize several typical results.
Thursday, February 5th, 2009
3:15 - 4:15 pm in UNA 125
Professor Lin Tan (West Chester University)
A Module approach to the Omega Process
I am going to finish MacMahon's examples this week, opting for the approach via module
structure, the approach of my choice at the moment.
Wednsday, February 11th, 2009
3:20 - 4:10 pm in UNA 158
XImena Catepillan (Millersville University) and
Professor Waclaw Szymanski (West Chester University)
INCA CULTURE AND MATHEMATICS
Ancient Inca, one of the Pre-Columbian civilizations, developed an advanced
culture. A part of that culture was mathematics based on decimal system. They
used mathematics, in particular, to build their 14,000 mile road structure and
monumental architecture. After an introduction to the Inca culture some
algorithms believed to be used by Inca to do computations with the help of a
``yupana" - an ancient calculating device - will be presented, as well as
classroom activities for the course ``Mathematics in Non-European Cultures" for
non-mathematics and science majors offered at Millersville University. All,
including the students, are welcome.
Thursday, February 12th, 2009
6:00 pm in UNA 162
Alex
Kouassi, Ph.D. (Group Director of Statistics, Schering-Plough Research Institute)
Clinical trials are an essential component
of drug development. They are instrumental in providing patients in need with
safe and effective therapies. But for a clinical trial to weed out unsafe or
ineffective drug compounds, the clinical team must
(1) Select
the proper endpoint and adequate design in order to answer as precisely as
possible the intended clinical question. Make use of appropriate randomization
and blindness methods to ensure baseline comparability and control allocation as
well as assessment biases. The target population must be carefully chosen to
ensure a high degree of homogeneity, and the treatment schedule must be well planned in order to detect acute
toxicities with short duration.
(2) Adopt
sound and valid statistical analysis methods. Ensure that interim analysis, if
any, is properly planned with clear stopping rules and a well defined data
monitoring committee. In addition, ensure that the handling of missing data is
well specified and all multiplicity issues are addressed.
In this presentation, we discuss some
basic clinical trial designs and examine some special topics that often arise
during the conduct and analysis of clinical trials. We close with a few words on
the importance of the design of a clinical trial as well as the role of the
statistician in the conduct of the trial.
Thursday, February 19th, 2009
3:15 - 4:15 pm in UNA 125
Professor Lin Tan (West Chester University)
A q-Analogue of the Omega Operator
I will discribe a q-analogue of MacMahon's generating functions in which
when all the variables (other than q) are set to 1, you get the
Hilbert-Serre series. (We'll start with symmetric functions as an
appetizer.)
Wednsday, February 25th, 2009
3:20 - 4:10 pm in UNA 125
Professor Shiv Gupta (West Chester University)
Interesting Rational Triangles
Thursday, February 26th, 2009
3:15 - 4:15 pm in UNA 125
Professor Lin Tan (West Chester University)
The Omega Process and Continued Fractions.
I will be talking about the
continued fraction method of getting a partial fraction decomposition of the
generating function (among two other methods) for treating the Omega when the
coefficients of the Diophantine inequalities are large.
If there is time, I will talk about Omega
corresponding to the inhomogeneous Diophantine inequalities/equations after
that.
Tuesday, March 10th, 2009
3:15 - 4:15 pm in UNA 125
Professor Scott Parsell (Butler University, Indianapolis)
Analytic Methods for Diophantine Problems
Wiles and Taylor recently proved the long-standing
conjecture that for every integer $k \geq 3$ the
Fermat equation
$x^k+y^k=z^k$ has no integral solutions other than the obvious ones with
$xyz=0$.
This provides an example of the general philosophy that diophantine
equations in few variables should
have few (if any) non-trivial solutions.
Here the notion of ``few variables" is viewed in relation to the
degree of
the problem---the Fermat equation of course has many non-trivial solutions when
$k=2$.
When the number of variables is sufficiently large in terms of the
degree, one expects a diophantine
equation to have many non-trivial
solutions unless there is some obvious reason why it should not.
We will
describe an analytic method, originally developed by Hardy and Littlewood, that
verifies this
expectation for a large class of interesting problems. For
example, the method can be used to show that
every positive integer is the
sum of a bounded number of $k$th powers and that every sufficiently large
odd integer is the sum of three primes. We plan to describe the essential
features and standard applications of the method and then highlight some
recent developments and open problems in this area.
Friday, March 13th, 2009
3:15 - 4:15 pm in UNA 125
Professor Miron Bekker (University of Missouri-Kansas City)
Positive Definite Kernels and Functions and Some Applications
Positive definite
kernels and functions play important role in many problems of pure
and
applied mathematics. In our talk we define notions of a positive definite
kernel and a
positive definite function and consider some of their
applications as well as extension
problems. Special attention is paid to
positive definite generalized Toeplitz kernels.
Thursday, March 19th, 2009
3:15 - 4:15 pm in UNA 125
Professor Fangyun Yang (University of California, Riverside)
Index Theory and Its Applications
Given a linear partial differential system, usually it is very hard or
impossible
to find the solutions. The critical insight of Atiyah and Singer
is to ask a slightly different
question: how many solutions are there? And
The Atiyah Singer Index Theorem gives a
nice answer: the number of solutions
depends on the shape (topology) of the region we
are working on. In this
talk, I will first explain Atiyah Singer Index Theorem. Then I will talk
about some of its generalizations on manifolds with singularities.
Monday, March 23rd, 2009
3:15 - 4:15 pm in UNA 125
Professor Silvius Klein (University of California, Irvine)
Spectral Problems for Discrete Quasi-Periodic Schroedinger Operators
I will describe the discrete quasi-periodic Schroedinger
operator and
some of its expected spectral properties (predicted in solid
state physics
for disordered systems that this operator models). I will
mention some of the
known results for the case of real analytic potential
functions. Then, I will
discuss my own results and research projects for
the case of more general
potential functions. I will also describe a
simpler model (that of a
one-dimensional quasi-crystal) that could become
an undergraduate research
project.
Wednsday, March 25th, 2009
3:20 - 4:10 pm in UNA 162
Jean Pedersen (Santa Clara University)
We will begin by showing how a systematic folding procedure, used on a straight strip of
paper can produce approximations to regular N-gons, for any N ≥ 3. Braided models
constructed from the folded strips of paper will be displayed to show the geometric
utility of this folding procedure.
We will then follow the paper-folding ideas in a natural way to discover some amazing
facts about numbers. In particular, our discussion will lead to a very elementary
algorithm for calculating, for a given odd positive integer b, the smallest positive integer
k such that b will exactly divide either 2 k +1 or
2 k —1. And the algorithm determines
whether the "+" or the "—" applies. Following this idea further we will be able to
discover an even more surprising fact about numbers -- that you will only learn about if
you attend the talk.
The models will be taken apart at the end of the talk demonstrating my "proof by
destruction" that the tetrahedron can be braided with 2 strips, the cube with 3 strips,
the octahedron with 4 strips, the icosahedron with 5 strips, and the dodecahedron with 6
strips.
Jean Pedersen is Professor of Mathematics and Computer Science at Santa Clara University. She is the
author (or co-author) of over 200 articles and 7 books. She was the 1997 recipient of a Distinguished
Teaching Award from the Northern California Section of the Mathematical Association of America.
For further information e-mail
mfisher@wcupa.edu
or
sgupta@wcupa.edu
Thursday, April 9th, 2009
3:15 - 4:15 pm in UNA 125
Professor Lin Tan
(West Chester University)
THE
OMEGA PROCESS - THE CONCLUSION
Professor Tan
concludes his series of talks on the Omega operator by describing a
"Master Theorem" that encompasses most of the identities Mac Mahon derives
from the Omega process.
Thursday, April 16th, 2009
3:15 - 4:15 pm in UNA 125
Professor Peter Zimmer (West Chester University)
An Introduction to Dirichlet Characters and
L-functions
Modular forms and automophric forms are examples of quantities that have both an
Euler product and a functional equation. The study of modular forms and
automorphic forms incorporate algebra, complex analysis, number theory and
representation theory. To see how such an object comes about, we will first
consider Dirichlet characters and L-functions. Dirichlet characters are
representations of Abelian groups and L-functions are similar to Riemann's zeta
function. We will introduce Dirichlet characters and L-functions
and derive their Euler product and functional equation.
Wednsday, April 22nd, 2009
3:20 - 4:10 pm in UNA 162
Doron Zeilberger (Rutgers University)
“To Stop or Not To Stop?”
In a recent fascinating article in American Scientist, Theodore Hill described a cointossing
game whose pay-off is the ratio of heads to the total number of throws. If right
now you have 5 heads and 3 tails, should you stop, collecting 5/8, or should you keep
playing, hoping to get a better score? No one knows. [Joint work with Luis Medina]
Doron Zeilberger is a Professor of Mathematics at Rutgers University. He received his PhD from the
Weizmann Institute of Science (Israel) in 1976. Professor Zeilberger has made important contributions to
the fields of hypergeometric summation and q-Series. The so-called Wilf-Zeilberger pair and Zeilberger's
algorithm are indispensable tools for summing hypergeometric series, and these techniques are used
extensively in modern computer algebra software. He was also the first to prove the elusive result in
combinatorial theory known as the alternating sign matrix conjecture, as well as a number of related
propositions. Professor Zeilberger was a co-recipient of the 1998 Steele Prize of the American
Mathematical Society for his research on hyper- geometric summation and the recipient of the 2004 Euler
Medal of the Institute of Combinatorics and its Applications.
For further information e-mail
mfisher@wcupa.edu
or
sgupta@wcupa.edu
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