For more information about this meeting, contact Sergei Tabachnikov.

Title: | Coarse Schottky Problem |

Seminar: | Department of Mathematics Colloquium |

Speaker: | Lizhen Ji, University of Michigan |

Abstract: |

An important space in algebraic geometry is the moduli space of compact Riemann surfaces (or algebraic curves) of genus at least 2 (or compact oriented hyperbolic surfaces), and an important arithmetic locally symmetric space is the Siegel modular space, which is the moduli space of principally polarized abelian varieties.
There is a natural map between them by associating each compact Riemann surface its Jacobian variety, which is a principally polarized abelian variety. The famous Schottky problem is to characterize or determine the locus of Jacobian varieties in the Siegel modular space.
In 1994, Buser and Sarnak showed that the Jacobian locus lies in a small neighborhood of the boundary of the Siegel modular space as the genus goes to infinity. Motivated by this, Farb raised the coarse Schottky problem: understand the size of the Jacobian locus in the sense of coarse geometry emphasized by Gromov, for example, in the asymptotic cone of the Siegel modular space.
In this talk, we will discuss a solution of this problem of Farb by showing that the Jacobian locus is coarsely dense in the Siegel modular space, and hence its image in the asymptotic cone is equal to the whole cone. (This is a joint work with Enrico Leuzinger). |

### Room Reservation Information

Room Number: | MB114 |

Date: | 04 / 09 / 2009 |

Time: | 04:00pm - 05:00pm |