I am an Assistant Professor at James Madison University. I received my Ph.D. in May 2007 from the University of Washington and subsequently served as a VIGRE Assistant Professor at the University of California, Davis. My research interests include algebraic and enumerative combinatorics related to the representation theory of Coxeter groups, Hecke algebras and quantum groups.
I am currently teaching Discrete Structures I Math 227 and Abstract Algebra II Math 431.
Previous clases include:
- Abstract Algebra Math 430
- Nature of Mathematics Math 103
- Calculus I Math 235
- Calculus II Math 236
- Calculus with Functions Math 231
Publications, (with descriptions)
- (with Laura Bradford, Meredith Harris, Alex Komarinski, Carly Matson, and Edwin O'Shea) The Lecture Hall Theorem via Abacus Diagrams arXiv:math.CO/1211.3702.
- (with Laura Taalman and Anthony Tongen) Solitaire Mancala Games and the Chinese Remainder Theorem arXiv:math.CO/1112.3593, to appear in the American Mathematical Monthly.
- (with Rebecca Field) Using carry-truncated addition to analyze add-rotate-xor hash algorithms arXiv:cs.DM/1303.4448, to appear in the Journal of Mathematical Cryptology.
- (with Alexander Woo) Mask formulas for cograssmannian Kazhdan--Lusztig polynomials arXiv:math.CO/1011.1110, Ann. Combin. 17 (1) (2013) 151-203.
- (with Christopher R. H. Hanusa) Abacus models for parabolic quotients of affine Weyl groups arXiv:math.CO/1105.5333, J. Algebra 361 (2012), 134-162.
- (with Anne Schilling) Affine structures and a tableau model for E_6 crystals arXiv:math.CO/0909.2442, J. Algebra 324 (9) (2010) 2512-2542.
- (with Hugh Denoncourt) The enumeration of maximally clustered permutations arXiv:math.CO/0704.3469, Ann. Combin. 14 (1) (2010) 65-84.
- (with Christopher R. H. Hanusa) The enumeration of fully commutative affine permutations arXiv:math.CO/0907.0709, European Journal of Combinatorics 31 (5) (2010) 1342-1359.
- 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.