

Brant Jones
Department of Mathematics and Statistics
James Madison University
60 Bluestone Drive, MSC 1911
Harrisonburg, VA 22807
email: jones3bc (a t) jmu (d o t) edu
office: 325 Roop Hall, 540 568.3802

I am an Associate Professor at James Madison University. I earned my Ph.D. in mathematics in 2007 from the University of Washington in Seattle and was selected for a three year postdoctoral VIGRE Fellowship at the University of California, Davis before moving to Virginia.
I've mentored over 18 students majoring in math and computer science through various undergraduate research projects. In 2013, I was a visiting researcher in the semester program on Combinatorial Representation Theory at the Institute for Computational and Experimental Research in Mathematics (ICERM). In 2016, I was awarded a sabbatical semester and participated in the workshop on Polyhedral Geometry and Partition Theory at the American Institute of Mathematics (AIM). I currently coordinate our department's William Lowell Putnam Competition team and serve as coPI (with Anthony Tongen) for the NSF grant that funds our department's summer Research Experiences for Undergraduates (REU) site.
My research interests include games, algorithms, algebraic structures, and enumerative combinatorics, particularly as related to the representation theory of reflection groups. I frequently write computer programs to assist my mathematial work.
I have also had a successful career outside the university, in software engineering and consulting.

Teaching
This semester I am teaching History of Mathematics (Math 415) and Discrete Structures (CS/Math 227).
Some of my previous classes include:
Nature of Mathematics Math 103 
Calculus III (Multivariable) Math 237 
Graph Theory and Combinatorics Math 353 
Putnam Problem Solving Seminar Math 485 
Calculus (with Functions) Math 231 
Discrete Mathematics Math 245 
Abstract Algebra I, II Math 4301 
Calculus I, II Math 2356 
Elementary Number Theory Math 310 
Advanced Linear Algebra Math 434 
Research
My present work usually involves undergraduates. If you are a student interested in algorithms/programming or mathematical research, feel free to send me an email. Most recently, I've been thinking about sequential decision making.
The library of papers is below. The ones marked with * are especially recommended for undergraduate readers.
* Solitaire Mancala Games and the Chinese Remainder Theorem (with Laura Taalman and Anthony Tongen)
* The Refined Lecture Hall Theorem via Abacus Diagrams (with Laura Bradford, Meredith Harris, Alex Komarinski, Carly Matson, and Edwin O'Shea)
* Rational generating series for affine permutation pattern avoidance
* Permutations, Pattern Avoidance, and the Catalan Triangle (with Derek Desantis, Rebecca Field, Wesley Hough, Rebecca Meissen, and Jacob Ziefle)
Results and conjectures on simultaneous core partitions (with Drew Armstrong and Christopher R. H. Hanusa)
Using carrytruncated addition to analyze addrotatexor hash algorithms (with Rebecca Field)
Mask formulas for cograssmannian KazhdanLusztig polynomials (with Alexander Woo)
Abacus models for parabolic quotients of affine Weyl groups (with Christopher R. H. Hanusa)
Affine structures and a tableau model for E_{6} crystals (with Anne Schilling)
The enumeration of maximally clustered permutations (with Hugh Denoncourt)
The enumeration of fully commutative affine permutations (with Christopher R. H. Hanusa)
An explicit derivation of the Möbius function for Bruhat order
A bijection on core partitions and a parabolic quotient of the affine symmetric group (with Chris Berg and Monica Vazirani)
Leading coefficients of KazhdanLusztig polynomials for Deodhar elements
KazhdanLusztig polynomials for maximallyclustered hexagonavoiding permutations
Embedded factor patterns for Deodhar elements in KazhdanLusztig theory (with Sara C. Billey)
Mathematical Software
Sage: I have contributed some code to
sage.combinat, particularly an initial implementation of the LenartPostnikov alcove path model for crystals.
liberiksson: A C++ library to perform fast computations on elements of Coxeter groups, used for some of my papers on KazhdanLusztig polynomials. More specifically, the code classifies the Deodhar elements of finite Coxeter groups by embedded factor containment, and verifies that the mu coefficients for KazhdanLusztig polynomials associated to these elements are always 0 or 1.