Frontiers in Mathematical Sciences
University of Isfahan - January 1-3, 2020
On Hodge-Euler Polynomials of Character VarietiesSpeaker:
Azizeh Nozad, IPM
Date, Time, and Venue: Wednesday, January 1 | 15:15-16:00 | Hall 1Abstract:
With the idea of symmetry, we can say that the presence and importance of the notion of groups and group actions (introduced by Galios and Lie) was realized in ancient times. Understanding of the quotient spaces turned out to be extremely useful both in algebraic and in geometric classification problems. These problems were greatly unified by the notion of moduli space, introduced by Riemann and developed by Mumford. In this talk we will introduce moduli spaces of representations of finitely presented group into a complex reductive Lie group, so called character varieties, and explain some techniques used in their study, mainly computations of more refined invariants such as Hodge-Euler polynomials. We will also give an overview of known explicit computations of these polynomials as well as some conjectures and present some open problems.