What can pushforward measures tell us about the geometry and singularities of polynomial maps?

Yotam Hendel will discuss how polynomial maps can be studied by examining the analytic behavior of pushforwards of regular measures under them over finite and local fields. 

The guiding principle is that bad singularities of a map are reflected in poor analytic behavior of its pushforward measures. Yotam will present several results in this direction, as well as applications to areas such as counting points over finite rings and representation growth. 

Based on joint work with I. Glazer, R. Cluckers, J. Gordon, and S. Sodin.