# Department Seminars and Colloquia

### Volumes of moduli spaces of complex algebraic curves

Algebra/Geometry/Topology Seminar

#### Peter Zograf

Institution: Steklov Institute, St. Petersburg
Date: Mon 12th October 2009
Time: 3:15 PM
Location: Cuming Theatre, Chemistry

Abstract: Abstract:
The moduli spaces of (pointed) complex algebraic curves carry a natural
Kaehler metric called the Weil-Petersson metric. The volumes of moduli
spaces relative to the WP metric are important special cases of Gromov-Witten
invariants that naturally arise in both mathematics and theoretical physics
(string theory). We describe a fast algorithm for computing WP volumes
leading to a comjectural large genus asymptotic formula that holds with a
remarkable accuracy. We also discuss the asymptotics of WP volumes of
more general moduli spaces of bordered Riemann surfaces studied by
Mirzakhani.