Algebra/topology seminar

Speaker: Weiyan Chen (University of Chicago)

Title: Twisted cohomology of braid groups and algebraic varieties over finite fields

Abstract: The theory of étale cohomology provides a bridge between two seemingly unrelated subjects: the cohomology of braid groups with twisted coefficients (topology), and the number of points on algebraic varieties over finite fields (arithmetic). In this talk, we will pass this bridge in both directions, applying topology to prove results in arithmetic, and vice versa. For example, we will use point-counting to prove a recurrence relation on the stable cohomology of the braid groups with twisted coefficients. We also use topology to calculate the average number of points on a random superelliptic curve over finite fields.