## Columbia Mathematics Department Colloquium

Analysis and geometry of moduli spaces of Riemann surfaces

by

# Lizhen Ji

## University of Michigan

Abstract:

Moduli spaces of Riemann surfaces are fundamental objects of

mathematics and have been intensively and extensively studied since

Riemann. A lot of work has been done on the algebraic geometry and

algebraic topology aspects of the moduli spaces. In this talk, I will

describe some problems and results on spectral analysis, Riemannian geometry

and geometric topology of the moduli spaces.

mathematics and have been intensively and extensively studied since

Riemann. A lot of work has been done on the algebraic geometry and

algebraic topology aspects of the moduli spaces. In this talk, I will

describe some problems and results on spectral analysis, Riemannian geometry

and geometric topology of the moduli spaces.