Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Jules Martel
Affiliation:

Toulouse
Date:

Mon, 2020-05-11 15:00 - 16:00 Zoom meeting ID: 919-9946-8404

Password: see email announcement or contact the seminar organisers

Abstract: A construction based on Drinfel'd's definition of quantum

groups produces representations for braid groups. Their extensions to

knot invariants, due to Reshetikhin--Turaev, recover the famous Jones

polynomial for instance. The topological meaning of these algebraic

constructions is often missing in the end. In this work we provide a

homological model for quantum representations of braids, adapted from

Lawrence theory. It is based on relative homologies of configuration

spaces of points with local coefficients. This model reaches the level

of knots as it offers an interpretation for colored Jones polynomials in

terms of Lefschetz numbers. This will be presented in the first part,

while in the second one we will pay attention to the quantum algebra

action. After an algebraic study of it, we will build its homological

analogue.

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/node/6994