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Lie Groups and Representation Theory Seminar

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Place: Graduate School of Mathematical Sciences, the University of Tokyo [ Access ]
Date: March 10 (Fri), 2017, 17:00-18:30
Place: Room 056, Graduate School of Mathematical Sciences, the University of Tokyo
Speaker: Lizhen Ji (University of Michigan, USA)
Title: Satake compactifications and metric Schottky problems
Abstract:
[ pdf ]
The quotient of the Poincare upper half plane by the modular group SL(2, Z) is a basic locally symmetric space and also the moduli space of compact Riemann surfaces of genus 1, and it admits two important classes of generalization:
  1. Moduli spaces M_g of compact Riemann surfaces of genus g>1,
  2. Arithmetic locally symmetric spaces \Gamma \ G/K such as the Siegel modular variety A_g, which is also the moduli of principally polarized abelian varieties of dimension g.
There have been a lot of fruitful work to explore the similarity between these two classes of spaces, and there is also a direct interaction between them through the Jacobian (or period) map

J: M_g --> A_g.

In this talk, I will discuss some results along these lines related to the Stake compactifications and the Schottky problems on understanding the image J(M_g) in A_g from the metric perspective.

(joint with topology seminar)

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© Toshiyuki Kobayashi