Algebraic properties of certain RT-TQFTs

Speaker: Yilong Wang

Date:    2023.1.9

Time:   15:30-17:00

Venue: BIMSA 1129B

Zoom:  537 192 5549     Passcode: BIMSA

Abtract：

Modular tensor categories (MTCs) are algebraic structures that produce Reshetikhin-Turaev type (2+1)-TQFTs. In this talk, we will briefly introduce the notion of a MTC and their associated RT-TQFT, and show how they are related to quadratic forms on finite abelian groups, quantum groups at roots of unity and quantum invariants of 3-manifolds. We will then explain how we study MTC/RT-TQFTs from their arithmetic properties, with an emphasis on the representation of the genus 1 mapping class group $SL(2, \mathbb{Z})$, which is closely related to the Weil representations of quadratic modules. Finally, we will report some of our results in this direction.

[BIMSA Topology Seminar]