Bernhard Riemann and his moduli space

Lizhen Ji (University of Michigan)

Thursday, March 8, 2018 4:00 pm
MONT 214

Though Riemann only published a few papers in his lifetime, he introduced many notions which have had long lasting impact on mathematics. One is the concept of Riemann surfaces, and another is the related notion of moduli space of Riemann surfaces.

The road to formulate precisely the moduli space M_g of compact Riemann surfaces of genus g and to understand its meaning is long and complicated, and mathematicians are still working hard to understand its structures and properties from the perspectives of geometry, topology, analysis etc. Its analogy and connection with locally symmetric spaces have provided an effective way to study these problems.

In this talk, I will describe some historical aspects which may not be so well-known and some recent results on the interaction between moduli spaces and locally symmetric spaces.