Permutations and polynomiality in algebra and topology

School of Mathematics Colloquium
Friday, December 9, 2011 - 4:00pm for 1 hour (actually 50 minutes)
Skiles 006
Benson Farb – University of Chicago
John Etnyre

Please Note: There will be a tea 30 minutes before the colloquium.

Tom Church, Jordan Ellenberg and I recently discovered that the i-th Betti number of the space of configurations of n points on any manifold is given by a polynomial in n. Similarly for the moduli space of n-pointed genus g curves. Similarly for the dimensions of various spaces of homogeneous polynomials arising in algebraic combinatorics. Why? What do these disparate examples have in common? The goal of this talk will be to answer this question by explaining a simple underlying structure shared by these (and many other) examples in algebra and topology.