# Algebra Seminar 2020

In the fall, the seminar will be still on Tuesday at 4pm. This seminar is held via Zoom with Meeting ID: 512 854 8536.

### Fall Quarter, 2020

- October 6,
**Victor Ostrik** (UO)

Two dimensional topological field theories and partial fractions
**Abstract**: This talk is based on joint work with M.Khovanov and Y.Kononov. By evaluating a topological field theory in dimension 2 on surfaces of genus 0,1,2 etc we get a sequence. We investigate which sequences occur in this way depending on the assumptions on the target category.

- October 13,
**Pablo Ocal** (Texas A&M)

Hochschild cohomology of general twisted tensor products
**Abstract**: The Hochschild cohomology is a tool for studying associative algebras that has a lot of structure: it is a Gerstenhaber algebra. This structure is useful because of its applications in deformation and representation theory, and recently in quantum symmetries. Unfortunately, computing it remains a notoriously difficult task. In this talk we will present techniques that give explicit formulas of the Gerstenhaber algebra structure for general twisted tensor product algebras. This will include an unpretentious introduction to this cohomology and to our objects of interest, as well as the unexpected generality of the techniques. This is joint work with Tekin Karadag, Dustin McPhate, Tolulope Oke, and Sarah Witherspoon.

- October 20,
**Ming Zhang** (UBC)

Verlinde/Grassmannian correspondence
**Abstract**: In the 90s’, Witten gave a physical derivation of an isomorphism between the Verlinde algebra of

of level

and the quantum cohomology ring of the Grassmannian

. In the joint work arXiv:1811.01377 with Yongbin Ruan, we proposed a K-theoretic generalization of Witten’s work by relating the

Verlinde numbers to the level

quantum K-invariants of the Grassmannian

, and refer to it as the Verlinde/Grassmannian correspondence.

The correspondence was formulated precisely in the aforementioned paper, and we proved the rank 2 case (n=2) there. In this talk, I will explain the background of this correspondence and its interpretation in physics. At the end of the talk, I will briefly discuss the main idea of the proof for arbitrary rank. A new technical ingredient is the virtual nonabelian localization formula developed by Daniel Halpern-Leistner.

- November 3,
**Michail Savvas** (UCSD)
- November 10,
**Ben Wormleighton** (WUSTL)
- November 17,
**Lucas Mason-Brown** (MIT)
- November 24,
**Pyongwon Suh** (Northwestern)
- December 1,
**Pablo Boixeda Alvarez** (MIT)

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