Homology of configuration spaces: application to quantum topology
Jules Martel (Max Planck Institute, Bonn)
Monday 8th March, 2021 16:00-17:00 Online
Abstract
R. Lawrence has constructed homological representations of braid groups using configuration spaces. In the early 1990's, the ambition of her work was to recover quantum invariants built by e.g. Drinfel'd, Jones, Witten (unified through Reshetikhin--Turaev works). Ten years later, S. Bigelow and D. Krammer showed Lawrence's representations to be faithful, and Bigelow finally recovered the Jones polynomial out of them. Today, quantum topology has been widely derived, producing a lot of low dimensional topological invariants. They keep their share of mystery due to their very algebraic construction via quantum representation theory. In this presentation we will enrich Lawrence construction so to recover more tools from representation theory. It sheds light on homological interpretation for quantum invariants of braids and knots.
The talk will be preceded by a tea time at 3:45pm. The Zoom link for the seminar is https://uofglasgow.zoom.us/j/91412568415 and the passcode is the genus of the two-dimensional sphere (4 letters, all lowercase).
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