Geometric Aspects of Bombieri–Lang Finiteness in Moduli Theory

报告人

Speaker

Kang Zuo 左康

Wuhan University

时间

Time

Fri., 10:00-11:00 am, May 29, 2026

地点

Venue

C548, Shuangqing Complex Building A

Geometric Aspects of Bombieri–Lang Finiteness in Moduli Theory

Motivated by the arithmetic Bombieri–Lang conjecture, we propose a program toward a geometric Bombieri–Lang type finiteness theory for moduli spaces of algebraic varieties. A crucial ingredient is a global form of Shing-Tung Yau’s Schwarz lemma over moduli spaces. We study the distribution of non-rigid loci in moduli spaces, inspired by the philosophy of the André–Oort conjecture. In particular, we discuss how hyperbolicity, curvature properties, and Hodge-theoretic structures may lead to geometric finiteness phenomena analogous to those predicted by the Bombieri–Lang conjecture in arithmetic geometry. We also compare this geometric Bombieri–Lang finiteness framework with recent work of Junyi Xie and Xinyi Yuan on geometric Bombieri–Lang type problems, and suggest the possibility of a unified approach. Based on joint work with K. Chen, T.Z. Hu, R.R. Sun and C.L. Yu.

About the Speaker

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 journals such as Invent. Math.，Duke Math.J.，JEMS，Crelle's Journal.