email: brant (a t) math (d o t) ucdavis (d o t) edu

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.

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

Previous clases include:

• Calculus Math 16B
• Combinatorics Math 145
• Algebraic Combinatorics Math 146
• Advanced Calculus Math 25
• Applied Linear Algebra Math 167

   2008 REU on Rational Generating Functions for Permutation Patterns
   2009 REU on Combinatorics of Affine Reflection Groups

• (with Anne Schilling) Affine structures and a tableau model for E_6 crystals arXiv:math.CO/0909.2442.
  
• (with Chris Hanusa) The enumeration of fully commutative affine permutations arXiv:math.CO/0907.0709, To appear in European Journal of Combinatorics.
  
• (with Hugh Denoncourt) The enumeration of maximally clustered permutations arXiv:math.CO/0704.3469, To appear in Annals of Combinatorics.
  
• An explicit derivation of the Mobius function for Bruhat order arXiv:math.CO/0904.4472, Order 26 (4) (2009) 319-330.
  
• (with Chris Berg and Monica Vazirani) A bijection on core partitions and a parabolic quotient of the affine symmetric group arXiv:math.CO/0804.1380, J. Combin. Theory Ser. A 116 (8) (2009) 1344-1360.
  
• Leading coefficients of Kazhdan--Lusztig polynomials for Deodhar elements arXiv:math.CO/0711.1391, J. Algebraic Combin. 29 (2) (2009) 229-260.
  
• Kazhdan--Lusztig polynomials for maximally-clustered hexagon-avoiding permutations arXiv:math.CO/0704.3067, J. Algebra 322 (10) (2009) 3459-3477.
  
• (with Sara C. Billey) Embedded factor patterns for Deodhar elements in Kazhdan-Lusztig theory arXiv:math.CO/0612043, Ann. Combin. 11 (3/4) (2007) 285-333.
  

• 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.