时间：2024年11月15日（星期五）14:00-16:00

Time：14:00-16:00, Friday, November 15 2024

地点/Venue：E10-212

主讲人: 武汉大学 左康

Speaker: Kang Zuo, Wuhan University

主讲人简介: 左康，武汉大学教授，曾先后任职于德国海德堡大学、香港中文大学和德国美因茨大学（W3教授-德国最高级别教授）。左康老师主要研究领域是代数几何里的霍奇理论、模空间以及算术几何。他在复代数簇基本群的表示、模空间的双曲性、Shimura子簇的刻画等重要问题上取得丰富的成果，文章被发表在Invent. Math.，Duke Math.J.，JEMS，Crelle's Journal等顶级数学杂志上。

Biography:Kang Zuo, professor at Wuhan University, has worked in Heidelberg University, the Chinese University of Hong Kong and the University of Mainz. His research interests include Hodge theory in algebraic geometry, moduli spaces, and arithmetic geometry. He has made great achievements in the representation of fundamental groups of complex algebraic varieties, hyperbolicity of moduli spaces, characterization of Shimura subvarieties and other important problems. His articles have been published in top mathematical magazines such as Invent. Math.，Duke Math.J.，JEMS，Crelle's Journal.

讲座主题/Title：Finiteness of families of higher dimensional varieties

讲座摘要/Abstract: We introduce notions of Moduli spaces of polarized smooth varieties, Kodaira-Spencer deformation map, and variation of pola Hodge structures. We recall the original Shafarevich conjecture on the finiteness of families of curves over fixed bases and with fixed degeneration loci. This conjecture has been proven by Parshin and Arakelov. We present a proof using the positivity on the moduli space of smooth projective curves.

We then discuss the Shafarevich program on a moduli space M of higher dimensional varieties with good minimal models.

We propose a conjecture on the Bombieri-Lang type finiteness of the set of maps into M. The crucial part of the conjecture is about the distribution of loci of non-rigid maps into M. We show the conjecture holds for those moduli spaces carrying local Torelli theorem and such that the Mumford-Tate group is absolutely simple and the Mumford-Tate domain is not a bounded symmetry domain of rank >1. We discuss various examples of loci of non-rigid map into moduli spaces of Calabi-Yau manifolds. The talk is based a joint paper with K. Chen, TZ. Hu and RR. Sun and a joint project with RR. Sun and CL. Yu.