讲座题目: Subvarieties on degenerations of separably rationally connected varieties

讲 座 人: 曲三太，清华大学丘成桐数学科学中心

讲座时间: 2021年12月21日(星期二)下午14：00

讲座地点: 数大学院A204会议室

专家简介:

曲三太，毕业于中国科学技术大学少年班学院，2020年于纽约州立大学石溪分校获得数学博士学位，导师为代数几何学家Jason Starr教授。2020年10月至今于清华大学丘成桐数学科学中心做博士后研究，研究方向为代数几何、有理连通簇和双有理几何。

讲座主要内容：

The Ax conjecture predicts that every PAC (pseudo-algracially closed) field is C1. This conjecture has been completely solved when the field has characteristic zero. Also, the conjecture is answered positively when the field contains an algebraically closed field. The arithmetic set up of Ax conjecture is closely related to the geometry of degenerations of Fano varieties in characteristic zero, and degenerations of separably rationally connected varieties in positive characteristics. This geometric set up predicts the existence of a geometrically irreducible subscheme on the degenerations. In this talk, we will give a brief review on known results about Ax conjecture and then talk about how to bound the dimensions of these geometrically irreducible subschemes on degenerations.