VERTEX ALGEBRAS AND DISC COUNTING FROM DIRAC-SEGAL HTQFT. DISCUSSION WITH DONGWOOK CHOA, I

Name: VERTEX ALGEBRAS AND DISC COUNTING FROM DIRAC-SEGAL HTQFT. DISCUSSION WITH DONGWOOK CHOA, I
Start: 2020-12-04T10:00:00+03:00
End: 2020-12-04T12:00:00+03:00
Location: No location set

Friday 4 Dec 2020, 10:00 → 12:00 Europe/Moscow

Description

Dear all, I and Dongwook Choa decided to discuss how vertex algebras come out from Dirac-Segal HTQFT and how holomorphic disc counting is related to HTQFT and A-I-B. We decided to make this discussion open, record a video and put it to open access. Everybody who are interested are welcome to participate in real time or watch the video.

It is a complementary material for the course Introduction to B-theory. As you remember, I promised to give complementary talks if there will be any interest or questions from the audience.

We do not know how far can we go. If this discussion would go well, we will continue in part II, otherwise we will stop at part I.

This discussion would take place on Friday, 4 of December, 3 pm Beijing time that is 10 am Moscow time, that is 8 am Paris time that is 2 am East coast that is 11 pm West coast (Thursday).

The topics we are going to discuss are:

1. How to get from HTQFT to vertex algebras in different dimensions

2. Three different representations of (H)TQFT:

Quadratic actions, current algebras and instantonic theories.

Relations among them.

3.Vertex algebras in these representations of (H)TQFT

4.Floer theory and Fukaya theory for Lagrangian branes, Fukaya A-infinity categories, Fukaya tropicalization for specific Lagrangians in cotangent space to the manifold.

5.Disc as a state and disc as a D-brane, deformations of the theory and cancellation of boundary anomaly. Kapustin-Orlov branes versus matrix factorization (a conjecture), problem of generalization of Floer theory to Kapustin-Orlov branes, enumerative problems in Fukaya theory

6.Conjecture for A-I-B approach on a disc, conjecture for mirror for disc with corners (explicit toric example), simplest A-infinity structure for 3 to 1 operations only (C^* simplification of Polyschuk A-infinity for elliptic curves)

I hope that discussions on these subjects can help mathematicians to understand what mathematical physicists are talking about.

Best regards, Andrey Losev