Braid groups, Burau representations, and algebraic curves

Geometry Topology Seminar
Monday, August 31, 2015 - 2:05pm
1 hour (actually 50 minutes)
Skiles 006
U Chicago
The theory of ├ętale cohomology provides a bridge between two seemingly unrelated subjects: the homology of braid groups (topology) and the number of points on algebraic varieties over finite fields (arithmetic). Using this bridge, we study two problems, one from topology and one from arithmetic. First, we compute the homology of the braid groups with coefficients in the Burau representation. Then, we apply the topological result to calculate the expected number of points on a random superelliptic curve over finite fields.