Mathematics

pdf Some words of inspiration

Research

Publications and Preprints

pdf Cell Decompositions of Hecke Traces and Link Polynomials
Extended abstract. Accepted to Proceedings of the 37th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC) (Sapporo), 2025.
+ N. Williams

arxiv Level-Rank Dualities from Lusztig Series and Affine Springer Fibers
+ T. Xue

arxiv The Hilb-vs-Quot Conjecture
+ O. Kivinen

arxiv Unipotent Elements and Twisting in Link Homology

arxiv From the Hecke Category to the Unipotent Locus

web arxiv Simple Braids Tend toward Positive Entropy
J. Knot Theory Ramifications, 33(11) (2024), 2450034, 12 pp.
+ L. Robitaille

web arxiv Rational Noncrossing Coxeter–Catalan Combinatorics
Proc. Lond. Math. Soc., 129(4) (2024), e12643, 50 pp.
+ P. Galashin, T. Lam, N. Williams

web Extremal Primes for Elliptic Curves
J. Num. Theory, 164 (2016), 282–298.
+ K. James, B. Tran, P. Wertheimer, D. Zantout

web arxiv Zeros of Dirichlet \(L\)-Functions over Function Fields
Comm. Num. Theory Phys., 8(3) (2014), 511–539.
+ J. Andrade, S. J. Miller, K. Pratt

Selected Slides

• pdf Affine Springer Fibers and Level-Rank Duality. UChicago Representation Theory Seminar. 1/7/25.
• pdf Fock Spaces, Braid Varieties, and Block Equivalences. Northeastern GPRT Seminar. 10/31/24.
• pdf Character Formulas from Lusztig Varieties and Affine Springer Fibers. WUSTL Combinatorics Seminar. 9/30/24.
• pdf Triply-Graded Link Homology and the Hilb-vs-Quot Conjecture. IASM Online Geometry and Physics Seminar. 1/22/23.
• pdf Catalan Combinatorics in Algebraic Geometry. MIT–Harvard–MSR Combinatorics Seminar. 2/15/23.
• pdf Braids, Unipotent Representations, and Nonabelian Hodge Theory. Oxford Algebra Seminar. 11/30/21.
• pdf Homotopy Equivalences of Varieties Built from Braids. UMass Representation Theory Seminar. 10/25/21.
• pdf From \(\mathbf{H}\) to \(\mathcal{U}\). UMass FRG Conference on Categorical Braid Group Actions and Categorical Representation Theory. 6/17/21.

Other Writing

Publications

web The Hodge Theory of Soergel Bimodules
Chapter 18 in Introduction to Soergel Bimodules. Ed. B. Elias, S. Makisumi, U. Thiel, G. Williamson. RSME Springer Series, 5 (2020), 347–367.
+ L. Taylor

Selected Slides

• pdf Uniformization of Principal Bundles. UChicago \(\text{Bun}_G\) Seminar. 2/22/23.
• pdf Higgs Bundles and Global Springer Theory. Edinburgh reading group on affine Springer fibers. 3/15/22.
• pdf What Gauss Knew about Knots and Braids. MIT IAP lecture. 1/20/21. Here are the accompanying problems and references.

Teaching