Bowen Lectures: Lecture 1: Symmetries of polynomial equations

Lecture | February 19 | 4:10-5 p.m. | Sutardja Dai Hall, Banatao Auditorium

 James McKernan, UC San Diego

 Department of Mathematics

The symmetries of systems of polynomial equations can be be understood in terms of the geometry of the variety of zeroes (or solution set) of the polynomials. Roughly speaking, there are 3 kinds of geometries corresponding to positive, zero and negative curvature giving rise to 3 different kinds of symmetry groups. In this lecture, I will discuss recent advances in algebraic geometry that lead to very precise results on the structure of these symmetry groups.