Time: 4:30 - 5:30 pm
Contact: Haihan Wu
Faculty Contact: Mee Seong Im, Mikhail Khovanov
The visitor talks are at the intersection of topology, algebra, geometry, category theory, mathematical physics, and related areas.
Weekly Social Events (everyone is welcome)
Department Afternoon Tea: Mondays, Tuesdays, and Thursdays at 4pm in Krieger 413
Department Wine and Cheese: Wednesdays at 4pm in Krieger 413
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.
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.
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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.
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