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 2014 Colloquium/Seminar Schedule

Each Thursday there will be a mathematics seminar (usually in UNA 120 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: Spring 2014, Fall 2013, Spring 2013, Fall 2012, Spring 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009, Spring 2009, Fall 2008, Spring 2008, Fall 2007, Spring 2007, Fall 2006, Summer 2006, Spring 2006.

Department of Mathematics
West Chester University
Fall 2014 Mathematics Colloquium presents

Bruce Berndt
University of Illinois at Urbana-Champaign

The Circle and Divisor Problems, Bessel Function Series, and Ramanujan's Lost Notebook

 

Wednesday, September 10, 2014 from 3:15 to 4:15PM, UNA 120

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.

For further information e-mail mfisher@wcupa.edu or sgupta@wcupa.edu

 

 

Department of Mathematics
West Chester University
Fall 2014 Mathematics Colloquium presents

URban Larsson

Dalhousie University

 

Combinatorial Games and Computability

 

Wednesday, October 29, 2014 from 3:15 to 4:15PM UNA 120

 

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.

For further information e-mail mfisher@wcupa.edu or sgupta@wcupa.edu

Department of Mathematics
West Chester University
Fall 2014 Mathematics Colloquium presents
Maciej Wojtkowski

University of Warmia and Mazury, Poland

Markov partitions and 1-dimensional tilings”

Tuesday, November 11, 2014 Time: TBA

Room: TBA

Abstract:

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.

 

 

For further information e-mail mfisher@wcupa.edu or sgupta@wcupa.edu

 

 

 

 

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