Organized by Mina Aganagic, Sujay Nair, Peng Zhou and Jasper van de Kreeke. Weekly on Mondays 2:10 PM (PT) at 402 Physics South. You are invited for lunch on the 4th floor of Physics South before the seminar. Subscribe to the mailing list. Join via zoom. Youtube video archive

Date	Speaker	Title
Sep 23	Catharina Stroppel	Towards a higher dimensional TQFT(I)
Sep 30	Catharina Stroppel	Towards a higher dimensional TQFT(II)
Oct 7	Yixuan Li	Symmetric products of punctured spheres and horizontal hilbert schemes
Oct 14	Eugene Gorsky	Trace of the affine Hecke category
Oct 21	Kifung Chan	3d Mirror Symmetry is Mirror Symmetry
Oct 28		no seminar
Nov 4		no seminar
Nov 18	Brian Williams	Higher dimensional Segal—Sugawara construction and fivebranes
Dec 2	Catherine Cannizzo	Homological mirror symmetry for theta divisors
Dec 9	Mauricio Romo	Mirror symmetry for Calabi-Yau singular double covers

Seminar archive: Spring 2025 Spring 2024, Fall 2023, Spring 2023, Fall 2022, Spring 2022, Fall 2021, Spring 2021, Fall 2020, Summer 2020, Spring 2020, Fall 2019, Spring 2019, Fall 2018, Fall 2017, Spring 2017, Fall 2016

A note to the speakers: This is a research seminar, intended for mathematicians and physicists. For the speaker to successfully reach the audience in both fields, it is important to explain, as clearly as possible: the motivations for the work, questions addressed, key ideas. The audience may fail to appreciate the glory of the result, otherwise.

Sep 23: Catharina Stroppel (University of Bonn)

Towards a higher dimensional TQFT: categorified quantum group invariants

This is the first of two talks. I will give an overview on algebraic categorification of tensors products of type A quantum group representations emphasising the role of (categorified) skew Howe duality. The results are in principle not new, but the focus will be on explaining the advantages and disadvantages of the existing approaches. In particular I like to illustrate why tensor products are supposed to be difficult and outline the limits of the existing construction. 

Sep 30th: Catharina Stroppel (University of Bonn)

Towards a higher dimensional TQFT:  a (braided) monoidal category of Soergel bimodules

Starting from braided monoidal categories of quantum group representations and categorification results one comes to the question whether categorification can be used to construct a corresponding braided monoidal 2-category. In this talk we start from the observation that the Hecke algebras for all symmetric groups taken together form a braided monoidal category that controls all quantum link invariants of type A. We then discuss the problem of categorification and present some answers using Soergel bimodule categories. This is partially based on joint work with Aaron-Maazel Gee, Leon Liu, David Reutter and Paul Wedrich.

Oct 7th: Yixuan Li (UC Berkeley)

Symmetric products of punctured spheres and horizontal hilbert schemes

This talk is based on joint work in progress with Mina Aganagic, Spencer Tamagni and Peng Zhou. We’ll discuss work in progress toward a homological mirror symmetry statement. The A side is the k-fold symmetric product of a double cover of the cylinder ramified at n points. The B side is a matrix factorization category on the k-th horizontal hilbert scheme of the resolved A_{n-1} surface. Time permitting, I’ll exploit the informal nature of this seminar to discuss potential applications to the relation between sl(2) and gl(1|1) link invariants.

Oct 14th: Eugene Gorsky (UC Davis)

Trace of the affine Hecke category

Abstract: The affine Hecke category, defined using affine Soergel
bimodules, categorifies the affine Hecke algebra. I will compare the
derived horizontal trace of the affine Hecke category with the elliptic
Hall algebra, and with the derived category of the commuting stack. In
particular, I will describe certain explicit generators for the trace
category and some categorical commutation relations between these. This
is a joint work with Andrei Negut.

Oct 21th: Kifung Chan(Chinese University of Hong Kong)

3d Mirror Symmetry is Mirror Symmetry

3d mirror symmetry is a duality for certain hyperkähler manifolds. This talk will explore its connections with 2d mirror symmetry, as a 3d analog of ‘Mirror Symmetry is T-duality’ by Strominger, Yau, and Zaslow, which described 2d mirror symmetry via 1d dualities. Based on joint works with Naichung Conan Leung.

Video Slide

Nov 18th: Brian Williams(Boston University)

Higher dimensional Segal—Sugawara construction and fivebranes

Abstract: The correspondence of AGT sets up, in part, a connection between six-dimensional superconformal theories and 2d CFT. We will give a mathematical construction of 2d CFT from 6d SCFT which involves recent progress in our understanding of the holomorphic twist 6d superconformal symmetry. We then turn to the question of enhancement of familiar structures in 2d CFT to 6d including the well-known Segal—Sugawara construction. Time permitting, I will also set up a Dolbeault enhancement of the AGT correspondence which probes coherent cohomology of the moduli space of instantons.

Dec 2nd: Catherine Cannizzo (UC Berkeley)

Homological mirror symmetry for theta divisors

Abstract: Symplectic geometry plays a crucial role in string theory through the lens of mirror symmetry, a duality that connects it to complex geometry. This connection is formalized in M. Kontsevich’s celebrated 1994 ICM conjecture on homological mirror symmetry (HMS), providing a powerful algebraic framework to study these dualities. While HMS has been established for mirrors of Calabi-Yau and Fano manifolds, recent efforts have extended its scope to mirrors of general type manifolds, which are central to my research. In this talk, we’ll explore HMS through the classic example of the 2-dimensional torus T^2. Building on this, we’ll discuss its generalization to higher-dimensional tori, and then to new results for hypersurfaces of tori, known as “theta divisors”. This work is in collaboration with Haniya Azam, Heather Lee, and Chiu-Chu Melissa Liu.

Dec 9th: Mauricio Romo (Shanghai Institute for Mathematics
and Interdisciplinary Sciences)

Mirror symmetry for Calabi-Yau singular double covers

Abstract: I will discuss a recent proposal for mirror symmetry of singular CY double covers, originally proposed by Hosono-Lee-Lian-Yau from the point of view of gauged linear sigma models. Concretely I will argue that a physics realization of noncommutative resolutions can be used to characterize the mirror of such singular double covers and make computation of B-brane central charges (mirror to period integrals) and other properties, very explicit. I will present other consequences and generalizations, as time allows.