EVENT DETAILS AND ABSTRACT

Title: Counting problems and homological stability
Speaker: Jesse Wolfson
Speaker Info: Chicago
Brief Description:
Special Note:
Abstract:

In 1970, Arnold showed that the ith homology of the space of unordered configurations of n points in the plane becomes independent of n for large n. A decade later, Segal extended Arnold's method to show that the ith homology of the space of degree n holomorphic maps from P^1 to itself also becomes independent of n for large n, and, moreover, that both sequences of spaces have the same limiting homology. We explain how, using Weil's number field/function field dictionary, one might have predicted this topological coincidence from easily verifiable statements about specific counting problems. We then discuss ongoing joint work with Benson Farb and Melanie Wood in which we use other counting problems to predict and discover new instances of homological stability in the topology of complex manifolds.