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Nathan Williams

Nathan Williams

Associate Professor - Mathematical Sciences
 
972-883-6476
FO 2.402C
Personal webpage
ORCID
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Professional Preparation

Ph.D. - Mathematics
University of Minnesota - 2013
B.A. - Mathematics
Carleton College - 2008

Research Areas

Dynamical algebraic combinatorics
Reflection and braid groups
Combinatorial representation theory
Catalan combinatorics

Publications

An elaborate new proof of Cayley’s formula 2025 - Journal Article
Cataland: Why the Fuß? 2025 - Journal Article
PERMUTAHEDRON TRIANGULATIONS VIA TOTAL LINEAR STABILITY AND THE DUAL BRAID GROUP 2025 - Other
ROWMOTION AND ECHELONMOTION 2025 - Other
Strange expectations in affine Weyl groups 2024 - Journal Article
Charmed roots and the Kroweras complement 2024 - Journal Article
The Ungar Games 2024 - Journal Article
Wiener Indices of Minuscule Lattices 2024 - Journal Article

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
Visiting Assistant Professor of Mathematics
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.

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
Mega Millions Interviewed by CBS DFW reporter Nick Starling for a segment on the $1.28 billion Mega Millions jackpot.
Bracketology
Bracketology Interviewed by WFAA Feature Reporter Sean Giggy for a segment on NCAA “Bracketology”.

Activities

Fall 2021 - BIRS Hybrid Workshop Organizer
Topic: Dynamical Algebraic Combinatorics.  Workshop webpage.
Fall 2021 - FPSAC Funding Coordinator
FPSAC webpage
Fall 2020 - BIRS Online Workshop Organizer
Topic: Dynamical Algebraic Combinatorics.  Workshop webpage.

Funding

New Techniques in Algebraic Combinatorics
$42,000 - Simons Foundation [2018/09–2023/08]
Simons Collaboration Grant for Mathematicians 585380
Graduate Student Combinatorics Conference 2018
$20,000 - National Science Foundation [2018/03–2019/02]
Grant Number 1801331