- Series
- Geometry Topology Seminar
- Time
- Monday, November 7, 2022 - 4:30pm for 1 hour (actually 50 minutes)
- Location
- ONLINE
- Speaker
- Amitesh Datta – Princeton University – amiteshd@princeton.edu – https://amiteshdatta.wixsite.com/amitesh-datta/
- Organizer
- Dan Margalit

How good of an invariant is the Jones polynomial? The question is closely tied to studying braid group representations since the Jones polynomial can be defined as a (normalized) trace of a braid group representation.

In this talk, I will present my work developing a new theory to precisely characterize the entries of classical braid group representations, which leads to a generic faithfulness result for the Burau representation of B_4 (the faithfulness is a longstanding question since the 1930s). In forthcoming work, I use this theory to furthermore explicitly characterize the Jones polynomial of all 3-braid closures and generic 4-braid closures. I will also describe my work which uses the class numbers of quadratic number fields to show that the Jones polynomial detects the unknot for 3-braid links - this work also answers (in a strong form) a question of Vaughan Jones.

I will discuss all of the relevant background from scratch and illustrate my techniques through simple examples.

https://gatech.zoom.us/my/margalit?pwd=b3RhY3pVZUdlRUR3S1FLZzhFR1RVUT09