Congruence subgroups of braid groups

Series
School of Mathematics Colloquium
Time
Friday, December 7, 2018 - 4:00pm for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Tara Brendle – University of Glasgow
Organizer
Dan Margalit
The Burau representation plays a key role in the classical theory of braid groups. When we let the complex parameter t take the value -1, we obtain a symplectic representation of the braid group known as the integral Burau representation. In this talk we will give a survey of results on braid congruence subgroups, that is, the preimages under the integral Burau representation of principal congruence subgroups of symplectic groups. Along the way, we will see the (perhaps surprising) appearance of braid congruence subgroups in a variety of other contexts, including knot theory, homotopy theory, number theory, and algebraic geometry.