Spring 2026
Time: 4:30 - 5:30 pm
Room: Gilman 119 (Mondays), Mergenthaler 111 (Tuesdays)
Contact: Haihan Wu
Faculty Contact: Mee Seong Im, Mikhail Khovanov
February 2 (Monday, Gilman 119): Mayuko Yamashita (Perimeter Institute for Theoretical Physics)
Title: Geometric engineering in Topological Modular Forms
Abstract: “Geometric engineering” is a terminology in physics, referring to processes creating interesting QFTs out of simple pieces, by sequence of basic geometric processes. I will explain my ongoing project to mimic that in elliptic cohomology theory, guided by Segal-Stolz-Teichner paradigm. I will explain the progress on the cases related to the K3 sigma model, with the motivation coming from the Mathieu moonshine.
February 10 (Tuesday, Mergenthaler 111): Yoon Seok (John) Chae (California Institute of Technology, Pasadena, CA)
Title: Knot complements, series invariants and Lie superalgebra
Abstract: Inspired by the categorification program for a numerical invariant of three-manifolds at roots of unity, series invariants for closed manifolds and for knot complements were introduced. This in turn motivated an extension of the series invariant of the former case to Lie superalgebras. It was recently generalized to knot complements. In this talk, we review the original series invariants and introduce the recent generalization and explore its properties and examples.
February 17 (Tuesday, Mergenthaler 111): Liron Speyer (Okinawa Institute of Science and Technology, Okinawa, Japan)
Title: Hecke algebras, KLR algebras, and James's conjecture
Abstract: I will give a brief account of the combinatorial representation theory of type A Iwahori–Hecke algebras, and their realisation as cyclotomic KLR algebras. In this story, I will largely focus on the decomposition number problem as one of the key problems in this field, and James's conjecture, which drove a lot of research until Williamson showed it to be false in 2013. While Williamson's counterexample is incredibly large, and beyond explicit computation, I recently discovered a new counterexample, which is of minimal size. I will explain this counterexample in the talk, as well as touching on how I found it.
March 3 (Tuesday, Bloomberg 276): Hyun Kyu Kim (Korea Institute for Advanced Study, Seoul, South Korea)
Title: Skein algebras of genus zero surfaces and quantized K-theoretic Coulomb branches
Abstract: The Kauffman bracket skein algebra of an oriented surface S is a quantization of the SL(2) character variety of S, and is generated by isotopy classes of framed links living in S times an interval, modulo skein relations. The relative skein algebra quantizes the relative character variety, fixing the classes of monodromy along small loops around punctures. We show that the relative skein algebra of a punctured surface of genus zero is isomorphic to the Braverman-Finkelberg-Nakajima quantized K-theoretic Coulomb branch, associated to a certain group G and representation N, built from a specific quiver. This gives a monoidal categorification of the genus zero relative skein algebra, which in particular yields a positive basis through the work of Cautis and Williams, partially answering a question posed by D. Thurston. Based on the joint work with Dylan Allegretti and Peng Shan, arXiv:2505.13332.
March 9 (Monday, Hodson 313): Ross Akhmechet (Columbia University, New York, NY)
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March 24 (Tuesday, Mergenthaler 111): Taketo Sano (RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences)
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March 31 (Tuesday, Mergenthaler 111): Joshua Sussan (Medgar Evers College, CUNY, Brooklyn, NY)
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April 6 (Monday, Gilman 119): Daniel Berwick-Evans (University of Illinois at Urbana-Champaign)
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April 13 (Monday, Gilman 119): Elijah Bodish (Indiana University Bloomington)
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April 23 (Thursday, TBD): Andrew J. Blumberg (Columbia University)
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