Department of Mathematics

West Chester University

Mathematics Information
Office: Room 101
25 University Avenue
West Chester, PA 19383
Phone (610) 436-2440
Fax (610) 738-0578
Email: Department Chair


Fall 2006 Colloquium/Seminar Schedule

Each Thursday during the semester there is a mathematics seminar (usually in Anderson 120 from 3:15-4:15). Over perhaps one or two semesters, we consider a selected topic and, beginning with basic definitions, work up to the point where we can discuss current research in the area and present research discoveries by department faculty members in the area. This seminar is open to all interested students and faculty at West Chester.

Occasionally outside speakers or WCU mathematics faculty present a talk in the mathematics colloquium, which may be on a different topic. (check this page for times and locations).

Previous Semesters: Summer 2006, Spring 2006,

In our weekly seminar for the Fall 2006 semester, we continue with the topic of Q-series. All talks are in Anderson 120 unless stated otherwise. See the abstracts below for details of colloquium talks.

Wednesday, September 13th, 2006
3:00 pm in 108 Anderson Hall
James Mc Laughlin (West Chester University)
Some Long Continued Fractions

Thursday, September 14th, 2006
3:15 pm in 120 Anderson Hall
Peter Zimmer (West Chester University)
Rogers's Second Proof, I

Wednesday, September 20th, 2006
11:00 am in Anderson 120
Bruce Berndt (University of Illinois at Urbana-Champaign)
The Five Strangest, Most Fascinating, Most Interesting Results in

Thursday, February 22nd, 2007
3:15 pm in 120 Anderson Hall
James Mc Laughlin (West Chester University)
The Analytic Version of the Rogers-Ramanujan Identities
Ramanujan's Lost Notebook

Abstract: Many of Ramanujan's results, especially from his lost notebook, are so strange and surprising that it would seem that no one else, either in the present or the future, would have had the foresight to discover them. Five entries from Ramanujan's lost notebook have been chosen for presentation and detailed discussion. Each of them is surprising. All have been proved, except for one (as of this writing). Most of these entries have their origins in number theory. The first 10 minutes of this talk will be devoted to a history of the lost notebook.

Wednesday, September 20th, 2006
3:00 pm in Anderson 103
Bruce Berndt (University of Illinois at Urbana-Champaign)
Ramanujan's Life and Notebooks

Abstract: Ramanujan was born in southern India in 1887 and died there in 1920 at the age of 32. He had only one year of college, but his mathematical discoveries, made mostly in isolation, have made him one of last century's most influential mathematicians. An account of Ramanujan's life will be presented. Most of Ramanujan's mathematical discoveries were recorded without proofs in notebooks, and a description and history of these notebooks will be provided. The lecture will be accompanied by overhead transparencies depicting Ramanujan, his home, his school, his notebooks, and those influential in his life, including his mother and wife.

Thursday, September 28th, 2006
Peter Zimmer (West Chester University)
Rogers's Second Proof, II

Wednesday, October 4th, 2006
3:00 pm in Anderson (room to be announced)
Andrew Sills (Rutgers)
Rogers-Ramanujan-Slater type identities

Abstract: The Rogers-Ramanujan identities are famous in mathematics not only for their intrinsic beauty, but also for their appearance in analysis, number theory, combinatorics, Lie algebras, and statistical mechanics. In the 1940's, W.N. Bailey discovered a mathematical result (now known as "Bailey's lemma") which can be used to prove the Rogers-Ramanujan identities easily, and to discover many identities of similar type via "Bailey pairs." Bailey's student, L.J. Slater, found about 90 Bailey pairs, which she use to produce a list of 130 Rogers-Ramanujan type identities. I have recently found, however, that these 90 Bailey pairs of Slater are not isolated results. In fact, using just three generalized "multiparameter Bailey pairs", and associated q-difference equations, I was able recover more than half of Slater's list. Furthermore, this more unified perspective made it possible to discover many new identities and provide natural combinatorial interpretations for many of the new and old identities.

Thursday, October 19th, 2006
Peter Zimmer (West Chester University)
Bailey Chains, II

Thursday, October 26th, 2006
Peter Zimmer (West Chester University)
Bailey Chains, III

Thursday, November 9th, 2006
Peter Zimmer (West Chester University)
Bailey Chains, IV

Thursday, November 16th, 2006
Peter Zimmer (West Chester University)
Applications of Bailey's Lemma

Thursday, November 30th, 2006
James Mc Laughlin (West Chester University)
The Bailey Lemma and Basic Hypergeometric Transformations, I

Thursday, December 7th, 2006
James Mc Laughlin (West Chester University)
The Bailey Lemma and Basic Hypergeometric Transformations, II