Algebraic Geometry Seminar

Motivic random variables and a cohomological stability conjecture

Speaker: Sean Howe, Stanford University

Location: Warren Weaver Hall 317

Date: Tuesday, December 5, 2017, 3:30 p.m.


We give a conjectural description of the asymptotic cohomology of the moduli space of smooth hypersurfaces of degree d in P^n with m marked points as d goes to infinity. Our conjecture is based on point-counting and Hodge-theoretic stabilization results, and can be thought of as the simplest cohomological stabilization conjecture explaining the independent binomial random variables that appear in these results. Our conjecture is also supported by an analogy with the stable cohomology of the moduli space of curves with marked points, which can be thought of as the simplest possible cohomology ring giving rise to independent Poisson random variables