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Lie Groups and Representation Theory
Seminar information archive ～10/09｜Next seminar｜Future seminars 10/10～
| Date, time & place | Tuesday 16:30 - 18:00 126Room #126 (Graduate School of Math. Sci. Bldg.) |
|---|
2017/03/10
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Lizhen Ji (University of Michigan, USA)
Satake compactifications and metric Schottky problems (English)
Lizhen Ji (University of Michigan, USA)
Satake compactifications and metric Schottky problems (English)
[ Abstract ]
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.
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.
