Speaker Introduction

Dr. Ruiran Sun is an Associate Professor at the School of Mathematical Sciences, Xiamen University. He received his bachelor’s degree in mathematics from Xi’an Jiaotong University in 2013 and earned his Ph.D. in 2021 from the University of Mainz. His research focuses on algebraic geometry and complex geometry.

Abstract

In his 1962 ICM talk I. R. Shafarevich proposed profound conjectures about the geometry and arithmetic of moduli spaces of genus g curves. While A. Parshin and A. Arakelov established the function-field case, the celebrated 1983 work of G. Faltings resolved the conjecture for number fields. In this talk, we will give a brief introduction to the moduli space of genus g curves and Shafarevich’s conjecture. We will further survey recent advances in the geometry of moduli spaces of polarized varieties, time permitting.