A computational perspective on the Burau representation

Tuesday, 11-June-2024 

Abstract

The Burau representation of the braid group has generated a lot of interest since its appearance almost a hundred years ago. One reason for this is its connection to low-dimensional topology. I'll survey these foundations and discuss some recent computational approaches to study the case of the four-strand braid group, where famously the faithfulness of the Burau representation is still open. This will include joint work with Joel Gibson and Geordie Williamson, and ongoing work with Francois Charton, Ashvni Narayanan and Williamson.