Algebraic and tropical moduli spaces

Algebraic and tropical moduli spaces

Algebraic Geometry Seminar

Melody Chan (Brown University, Mathematics)

Wednesday, August 28, 2019 -
3:15pm to 4:15pm
Location: 
119 Physics

The moduli space of genus g Riemann surfaces, denoted M_g, has been studied for more than a century, yet much of its geometry is still a mystery. For example, in the 1980s Harer and Zagier showed that the Euler characteristic (up to sign) grows super-exponentially with g---yet most of this cohomology is not explicitly known. I will give an introduction to M_g, and discuss recent results with Soren Galatius and Sam Payne finding exponentially growing cohomology in degree 4g-6, disproving a conjecture of Kontsevich; and a proof, with Carel Faber, Galatius, and Payne, of a formula for top-weight Euler characteristic of M_{g,n} conjectured by Zagier.

Last updated: 2020/07/05 - 10:32pm