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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
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I am a 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 27 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). In 2019, I led a Research Experiences for Undergraduate Faculty (REUF) workshop at ICERM.
In 2021, a paper I co-authored with Laura Taalman and Anthony Tongen was cited by Don Knuth in The Art of Computer Programming (volume 4, pre-fascicle 14a on bipartite matching). I have previously served as PI/co-PI for NSF grants that funded our department's summer Research Experiences for Undergraduates (REU) site from 2017 through 2023, and this site presently continues under the leadership of Alex Capaldi and David Duncan. I currently coordinate our department's William Lowell Putnam Competition team.
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 and have had a successful career outside the university in software engineering/consulting.
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Teaching
Some of my previous classes include:
Nature of Mathematics (Strategy and Games) Math 103 |
Calculus III (Multivariable) Math 237 |
Stochastic Processes Math 423 |
Introductory Calculus Math 205, 231 |
Discrete Mathematics Math 245 |
Abstract Algebra I, II Math 430-1 |
Elementary Statistics Math 220 |
Elementary Number Theory Math 310 |
Advanced Linear Algebra Math 434 |
Discrete Structures CS/Math 227 |
Graph Theory and Combinatorics Math 353 |
Topology Math 435 |
Calculus I, II Math 235-6 |
History of Mathematics Math 415 |
Putnam Problem Solving Seminar Math 485 |
Presentations
Colloquium talk at the University of Maryland, Baltimore County October 22, 2021 (pandemic-era video talk)
Spring MAA MD-DC-VA section meeting April 13, 2019 (
transcript)
Research
My present work frequently involves undergraduates. If you are a student interested in algorithms/programming or mathematical research, send me an email!
The library of papers is below. Collaborators marked with * are undergraduate researchers.
Integer diagonal forms for subset intersection relations (with Joshua E. Ducey, *Lauren Engelthaler, *Jacob Gathje, *Izzy Pfaff, and *Jenna Plute)
Strategy-indifferent games of best choice (with Katelynn D. Kochalski, Sarah Loeb and Julia C. Walk)
Weighted games of best choice
Opportunity costs in the game of best choice (with *Madeline Crews, *Kaitlyn Myers, Laura Taalman, *Michael Urbanski, and *Breeann Wilson)
Avoiding patterns and making the best choice
Positional strategies in games of best choice (with *Aaron Fowlkes)
Rational generating series for affine permutation pattern avoidance
Results and conjectures on simultaneous core partitions (with Drew Armstrong and Christopher R. H. Hanusa)
The refined lecture hall theorem via abacus diagrams (with *Laura Bradford, *Meredith Harris, *Alex Komarinski, *Carly Matson, and Edwin O'Shea)
Solitaire Mancala Games and the Chinese Remainder Theorem (with Laura Taalman and Anthony Tongen)
Permutation pattern avoidance and the Catalan triangle (with *Derek Desantis, Rebecca Field, *Wesley Hough, *Rebecca Meissen, and *Jacob Ziefle)
Using carry-truncated addition to analyze add-rotate-xor hash algorithms (with Rebecca Field)
Mask formulas for cograssmannian Kazhdan--Lusztig 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 E6 crystals (with Anne Schilling)
The enumeration of fully commutative affine permutations (with Christopher R. H. Hanusa)
The enumeration of maximally clustered permutations (with Hugh Denoncourt)
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 Kazhdan--Lusztig polynomials for Deodhar elements
Kazhdan--Lusztig polynomials for maximally-clustered hexagon-avoiding permutations
Embedded factor patterns for Deodhar elements in Kazhdan-Lusztig theory (with Sara C. Billey)
Mathematical Software
Sage: I have contributed some code to
sage.combinat, particularly an initial implementation of the Lenart--Postnikov 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 Kazhdan--Lusztig polynomials. More specifically, the code classifies the Deodhar elements of finite Coxeter groups by embedded factor containment, and verifies that the mu coefficients for Kazhdan--Lusztig polynomials associated to these elements are always 0 or 1.