Vahid Shahverdi: Algebraic geometry with "random" flavor

Abstract:

In this talk, I will introduce some basic tools and notions in algebraic geometry, measure theory, and representation theory. Then, I will talk about two concepts of degree and volume of an algebraic set to answer the following questions:

1. How many zeros of a random polynomial are real?
2. What is the topology of random hypersurfaces?

This is a pre-colloquium targeted towards master and PhD students as a preparation for Antonio Lerario's talk  at 15:15.