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I am a VIGRE assistant professor interested in algebraic and enumerative combinatorics related to the representation theory of Coxeter groups, Hecke algebras and quantum groups. I received my Ph.D. in May 2007 at the University of Washington where my thesis advisor was Sara Billey.
Recent Projects
This year at UC Davis, I am running a Research Focus Group (RFG) on Applications of Representation Theory. One of our activities will be a topics course that I am teaching during Winter quarter.
During August 2009, I ran a Research Experience for Undergraduates (REU) on Combinatorics of Affine Reflection Groups.
Some conferences from the recent past and future:
Formal Power Series & Algebraic Combinatorics 2010
Algebraic Combinatorics at the SIAM Conference on Discrete Mathematics, June 2010
Joint Mathematics Meetings, January 2010
MAA MathFest 2009
Formal Power Series & Algebraic Combinatorics 2009
Permutation Patterns 2009
Geometric Representation Theory and Extended Affine Lie Algebras, Summer 2009
Teaching
Previous clases include:
Research Experiences for Undergraduates
2008 REU on Rational Generating Functions for Permutation Patterns
2009 REU on Combinatorics of Affine Reflection Groups
Papers, (with descriptions)
Software
- liberiksson C++ library
An expanded version liberiksson is available. This software implements a "numbers game" of Kimmo Eriksson, as described in his Ph.D. thesis and "Combinatorics of Coxeter groups" by Bjorner--Brenti. There are also client programs which classify the Deodhar elements of finite Coxeter groups by embedded factor containment, and verify that the mu coefficients in Kazhdan--Lusztig polynomials associated to these elements are always 0 or 1. The software also supports ad hoc calculations of these Kazhdan--Lusztig basis elements and the underlying combinatorial model due to Deodhar.
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