Winter 2012

Date	Speaker and Title
January 18	Joey Lee, University of Illinois - Chicago Polynomial automorphism in arithmetic dynamics Abstract: Polynomial automorphism is one of popular topics in various field. In this talk, we introduce new field 'arithmetic dynamics' and show some results in arithmetic dynamics for polynomial automorphisms: the Canonical height, equidistribution of periodic points, finiteness of commuting maps of bounded degree and the skew canonical height function.
February 1	Li Li, Oakland University Singularities of Schubert Varieties Abstract: The talk will focus on two invariants of Schubert varieties which are polynomials defined on pairs of permutations in the symmetric group. The first invariant is the celebrated Kazhdan-Lusztig polynomials defined using Hecke algebras. The second invariant is the h-polynomials of the local rings of Schubert varieties. We introduced a combinatorial concept called "drift configuration" which characterizes the second invariant for covexillary Schubert varieties, and we use this characterization to give a relation between the above two invariants. This is based on joint work with Alex Yong.
March 7	Sug Woo Shin, MIT Families of automorphic L-functions Abstract: I will survey some conjectures and statistical results on families of automorphic forms and their L-functions, for instance concerning the equidistribution of local invariants and zeros of L-functions. Then I will report on a recent result with Nicolas Templier.
March 21	Dylan Rupel, University of Oregon Title: Quantum Cluster Characters Abstract: In this talk I will describe the non-initial cluster variables in a quantum cluster algebra in terms of the representation theory of a corresponding quiver. Time permitting, I will explain why quantum cluster characters should have ever been discovered by realizing them as the image under a certain algebra homomorphism from the Ringel-Hall algebra of the quiver to the initial quantum torus.
April 4	David Gluck, Wayne State University Title: Rational and 2-rational character values Abstract: An old but recently disproved conjecture proposed that if every irreducible character of a finite group G is rational valued, then the same is true of a 2-Sylow subgroup of G. I will discuss recent related results and conjectures.

Fall 2011

Date	Speaker and Title
October 4	Kyungyong Lee, Wayne State University A combinatorial formula for cluster variables of rank two Abstract
Friday October 7, 2pm	Nick Loehr, Virginia Tech Parking Functions, Trees, and Diagonal Harmonics Abstract
October 18	Suho Oh, University of Michigan Total Positivity and Weakly Separated Sets Abstract
November 15	Brian Smithling, University of Toronto On local models for Shimura varieties Abstract
November 29	Mark Lewis, Kent State University An overview of character degree graphs of finite groups Abstract