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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.
Teaching
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.
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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