Mathematics

Research

pdf Some words of inspiration

Papers

• Braids, Springer Actions, and Nonabelian Hodge Theory (2023). In preparation.
• arxiv pdf Level-Rank Dualities from \(\Phi\)-Harish-Chandra Series and Affine Springer Fibers (2023).
  + T. Xue
  
• arxiv pdf The Hilb-vs-Quot Conjecture (2023).
  + O. Kivinen
  
• arxiv pdf Simple Braids Tend toward Positive Entropy (2023).
  + L. Robitaille
  
• arxiv pdf Unipotent Elements and Twisting in Link Homology (2022).
• arxiv pdf Rational Noncrossing Coxeter–Catalan Combinatorics (2022).
  + P. Galashin, T. Lam, N. Williams
  
• arxiv pdf From the Hecke Category to the Unipotent Locus (2021).
• 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
  Here is a blog post by Terence Tao that discusses our work.

Selected Slides

• 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

Papers

• 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