Nathan Williams

Nathan Williams

Assistant Professor - Mathematical Sciences
 
972-883-6476
FO 2.402C
Personal webpage
ORCID
Tags: algebraic combinatorics arising within reflection groups geometric group theory representation theory

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

Semidistrim Lattices 2023 - Journal Article
Fixed points of parking functions 2023 - Journal Article
Bijecting hidden symmetries for skew staircase shapes 2023 - Journal Article
Crystal pop-stack sorting and type A crystal lattices 2022 - Journal Article
Rational Noncrossing Coxeter-Catalan Combinatorics 2022 - Other
Pop, Crackle, Snap (and Pow): Some Facets of Shards 2022 - Other
Coxeter pop-tsack torsing 2021 - Other
Crystal pop-stack sorting and type a crystal lattices 2021 - Other

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