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 and Hecke algebras. I received my Ph.D. in May 2007 at the University of Washington where my thesis advisor was Sara Billey.

Summer 2009 Conferences:
  Geometric Representation Theory and Extended Affine Lie Algebras
  Permutation Patterns
  Formal Power Series & Algebraic Combinatorics
  MathFest

In 2009-10, I will be running a Research Focus Group (RFG) on Applications of Representation Theory.

Previous clases include:

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

• (with Chris Hanusa) The enumeration of fully commutative affine permutations arXiv:math.CO/0907.0709
  
• An explicit derivation of the Mobius function for Bruhat order arXiv:math.CO/0904.4472
  
• (with Hugh Denoncourt) The enumeration of maximally clustered permutations arXiv:math.CO/0704.3469
  
• (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
  
• 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
  
• (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.