“Motivic Random Variables and Random Matrices”

As first shown by Katz-Sarnak, the zero spacing of L-functions of smooth plane curves over finite fields approximate the infinite random matrix statistics observed experimentally for the zero spacing of the Riemann-Zeta function (arbitrarily well by first taking the size of the finite field to infinity, and then the degree of the curve to infinity). The key geometric inputs are a computation of the image of the monodromy representation and Deligne’s purity theorem, which ensures that only the zeroth cohomology group of irreducible local systems will contribute asymptotically to the statistics. In this talk, we explain how higher order terms (i.e. the lower weight part of cohomology) can be computed starting from a simple heuristic for the number of points on a random smooth plane curve.

### Details

Algebraic Geometry SeminarSean Howe (Stanford)

April 27, 2018

4:00 PM - 5:00 PM

More information available at:

http://mathematics.stanford.edu/algebraic-geometry-seminar/

### Location

Math 383-N450 Serra Mall

Bldg. 380

Room 383-N

Stanford CA 94305