BGHK-Seminar 25.10.2019

Khovanov and Seidel gave in 2000 an action of the classical braid group on a category of algebraic nature that categorifies the Burau representation. They proved the faithfulness of this action through the study of curves in a punctured disk (while Burau representation is not faithful for braids with five strands or more). In a recent article with Anne-Laure Thiel and Emmanuel Wagner, we extended this result to the braid group of the cylinder. The work of Khovanov and Seidel also had a symplectic aspect that we now generalize. In this talk, I will explain the strategy and tools to get a symplectic monodromy in our case and prove its injectivity. If time permits, I will explain how this action lifts to a symplectic categorical representation on a Fukaya category that should be related to the algebraic categorical representation. This is a joint work in progress with Anne-Laure Thiel and Emmanuel Wagner.

Freitag, den 25. Oktober 2019 um 14.15 Uhr, in Mathematikon, INF 205, Hörsaal Freitag, den 25. Oktober 2019 at 14.15, in Mathematikon, INF 205, Hörsaal

Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. Peter Albers