Geometry & Topology Seminar

Date: Wednesday, 11 November 2026

Time: 12noon-1pm 

Speaker: Grace Garden (Sorbonne University)

Location: SMRI Seminar Room (Macleay A12 Room 301)

Title: Burau representations and the mapping class group of the twice-punctured torus 

Abstract: The twice-punctured torus S_(1,2) occupies an intermediate position between 
surface mapping class groups, braid groups, and surface groups. In this talk, we use 
these connections to study representations from the mapping class group of the 
twice-punctured torus PMod(S_(1,2)) to SL(3, C). A particular focus is placed on those 
coming from the Burau representations, a famous family of representations classically 
defined on braid groups. Our main result is a classification of representations from 
PMod(S_(1,2)) to SL(3, C) up to conjugacy. If time permits, we will also give a survey 
on specific parameters for Burau representations with geometric meaning. This is joint 
work with Elisha Falbel and Antonin Guilloux.