During the Fall 2026 quarter, all of our meetings will be held in-person in 268 Skye Hall, primarily on Tuesdays.
Talks will run from 12:30-1:30pm unless otherwise indicated, but feel free to show up early for socializing with the speaker.
Current organizers: Carl Mautner
Fall 2026 schedule
September 29, 2026
Carl Mautner (UC Riverside)
Title: Determinants of q-intersection matrices
Abstract: In this talk I will describe two matrices associated to real affine hyperplane arrangements: the Varchenko matrix V introduced in the 90’s and a q-intersection matrix introduced more recently in joint work with Eberhardt. We gave a conjectural combinatorial formula for the determinant of the q-intersection matrix which I will describe and motivate. Around the same time, Thomas Lam gave a similar looking conjecture for the determinant of a submatrix of V^{-1}. In forthcoming joint work with Jens Eberhardt, we prove both Lam’s conjecture and our own using the geometry of the complexified hyperplane arrangement complement, powerful results of Lam and Douai-Terao/Loeser-Sabbah/Varchenko, and an algebraic Koszul duality argument.
(Full disclosure: both conjectures are stated in the setting of oriented matroids. We prove only the realizable case.)
October 6, 2026
Monica Vazirani (UC Davis)
Title: Skeins on tori
Abstract: The G-skein module (technically, a completion of it) for the 3-torus is finite dimensional by a result of Gunningham-Jordan-Safronov. For G= GL_N and SL_N, there is a lovely combinatorial formula for these dimensions in terms of the partitions of N. Our formula arises from studying skeins on the 2-torus via the representation theory of the double affine Hecke algebra (DAHA) of type A and its connection to quantum D-modules. Using the DAHA, we also prove that all tangles in the relative N-point skein algebra are in fact equivalent to linear combinations of braids, modulo skein relations. I will discuss these results.
This is joint work with Sam Gunningham and David Jordan.
October 13, 2026
Student talks: Luis Palacios Vela, Jonathan Cervantes and Oliver Waite
Oliver's Title: Introduction to Entropic Certainty
Oliver's Abstract: In this talk I introduce the Schrödinger representation of the Heisenberg group along with a few of its important properties. After reviewing some definitions from operator algebras, I define the position and momentum algebras and their respective quantizations. There is then a pair of dual conditional expectations arising from cyclic actions of Heisenberg group elements on the quantized position algebra and its commutant. I will conclude by discussing some implications of this duality on the relative entropy, including the entropic certainty relation of Hollands--Xu.
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Jonathan's Title: Cellular algebras and the Schur algebra
Jonathan's Abstract: Graham and Lehrer introduced cellular algebras, which come equipped with a basis, indexed by a poset, and a compatible anti-involution. Multiplication shears this basis along one direction of the poset—giving nested ideals and a way to classify simple modules. The Schur algebra with Green's codeterminant basis is a well-known example.
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Luis's Title: Principal and magical sl_2 triples
Luis's Abstract: I'll give an introduction to what are principal and magical triples, and how both are related. We'll cover some examples, and we'll mention its relation to real Lie groups.
October 20, 2026
Lucas Gagnon (USC)
Title: From quasisymmetry to noncrossing combinatorics
Abstract: I will survey my recent work on quasisymmetric polynomials through the lens of three combinatorial objects: permutations, binary plane forests, and noncrossing partitions. Permutations give an origin story in the Schubert expansion problem for Hessenberg varieties. Forest polynomials solve this problem by connecting it to the ring of quasisymmetric functions, in various forms. Finally, noncrossing partitions provide a wide-reaching generalization of this phenomenon to arbitrary reductive groups. This talk is based on joint work with subsets of Bergeron, Nadeau, Tewari, Spink, Woo, and Zhuang.
October 27, 2026
Linus Setiabrata (MIT)
Title: TBA
Abstract: TBA
November 3, 2026
Eugene Gorsky (UC Davis)
Title: Double Dyck path algebras for arbitrary quivers
Abstract: In the course of their proof of Shuffle Theorem in algebraic combinatorics, Carlsson and Mellit introduced a remarkable algebra A_{q,t} and its cousin B_{q,t}. Later work revealed interesting connections of the algebra B_{q,t} with the elliptic Hall algebra and parabolic Hilbert schemes of points. I will describe a generalization of B_{q,t} for an arbitrary quiver Q and outline its connections with the K-theoretic Hall algebra of Q and parabolic quiver varieties. This is a joint work with Nicolle Gonzalez and Jose Simental.
November 10, 2026
Alexis Leroux-Lapierre (SLMath)
Title: TBA
Abstract: TBA
November 17, 2026
Student Talks II
Title: TBA
Abstract: TBA
November 24, 2026
Student talks III
Title: TBA
Abstract: TBA
December 1, 2026
David Jordan (University of Edinburgh)
Title: TBA
Abstract: TBA