Geometry, Topology and Dynamics Seminar
Benson Farb
University of Chicago
Stability, braid groups, and the counting of polynomials
Abstract: If you pick a degree d polynomial in F_q[x] at random, how many
linear factors do you expect it to have? The answer depends on the degree d,
but as degree tends to infinity the answer actually converges, to 1/(1+1/q).
In this talk I will explain this convergence as part of a general dictionary between:
(1) Counting problems about polynomials over finite fields F_q.
(2) The cohomology of braid groups.
The stability of (1), as in the example above, corresponds to "representation stability" in (2). This is joint work with Thomas Church and Jordan Ellenberg.
Much of the talk should be understandable to undergraduates.
Monday April 29, 2013 at 3:00 PM in SEO 636