Ph.D. - Mathematics
University of Minnesota - 2013
Nathan Williams
Associate Professor - Mathematical Sciences
Professional Preparation
B.A. - Mathematics
Carleton College - 2008
Carleton College - 2008
Research Areas
Dynamical algebraic combinatorics
Reflection and braid groups
Combinatorial representation theory
Catalan combinatorics
Publications
Awards
Credential in Effective College Instruction (https://badgr.com/public/assertions/PMQK9PK9Rt6RxamlZ-3fPg) - The Association of College and University Educators [2021]
Outstanding Teaching Award for Tenure-Track Faculty - University of Texas at Dallas - School of Natural Sciences and Mathematics [2020]
Appointments
Assistant Professor of Mathematical Sciences
University of Texas at Dallas [2017–Present]
School of Natural Sciences and Mathematics
University of Texas at Dallas [2017–Present]
School of Natural Sciences and Mathematics
Visiting Assistant Professor of Mathematics
University of California, Santa Barbara [2016–2017]
Supervisor: Jon McCammond
University of California, Santa Barbara [2016–2017]
Supervisor: Jon McCammond
Postdoctoral Researcher
Laboratoire de Combinatoire et d’Informatique Mathématique [2013–2016]
Université du Québec à Montréal, Canada Supervisors: François Bergeron, Christophe Hohlweg, Franco Saliola, Hugh Thomas.
Laboratoire de Combinatoire et d’Informatique Mathématique [2013–2016]
Université du Québec à Montréal, Canada Supervisors: François Bergeron, Christophe Hohlweg, Franco Saliola, Hugh Thomas.
Presentations
Catalan Combinatorics
2022/05–2022/05 We solve two open problems in Coxeter-Catalan combinatorics. First, we introduce a family of rational noncrossing objects for any finite Coxeter group, using the combinatorics of distinguished subwords. Second, we give a type-uniform proof that these noncrossing Catalan objects are counted by the rational Coxeter-Catalan number, using the character theory of the associated Hecke algebra and the properties of Lusztig's exotic Fourier transform. We solve the same problems for rational noncrossing parking objects. This is joint work with Pavel Galashin, Thomas Lam, and Minh-Tâm Quang Trinh. (https://arxiv.org/abs/2208.00121)Semidistrim Lattices
2021/11–2021/11 We introduce semidistrim lattices, a simultaneous generalization of semidistributive and trim lattices that shares many of their common properties. This is joint work with Colin Defant. (https://arxiv.org/abs/2111.08122)News Articles
Mega Millions
Interviewed by CBS DFW reporter Nick Starling for a segment on the $1.28 billion Mega Millions jackpot.
Bracketology
Interviewed by WFAA Feature Reporter Sean Giggy for a segment on NCAA “Bracketology”.