摘要：In this talk, we are mainly concerned with the geometry of rational curves on algebraic varieties. Our main object of study is rationally connected varieties, a kind of varieties that contain “plenty” of rational curves. It was shown by Koll?ar-Miyaoka-Mori that a kind of “smoothing of comb” technique is available on this kind of varieties. We firstly show a most general form of this kind of “smoothing of comb” technique exists, which extends all the “smoothing of comb” techniques in the literature before. Then we apply this generalized technique to study the geometry of forgetful maps between moduli spaces of stable maps and twisted stable maps to rationally connected varieties. As a result, we solve several open questions on topology, geometry and arithmetic of rationally connected varieties.
报告人简介： 于2010年获中国科学技术大学数学与应用数学专业学士，于2014年获美国普林斯顿大学数学专业博士，从2014年至今先后在美国普林斯顿高等研究院数学学院、美国加州大学洛杉矶分校数学系以及德国美因茨大学数学系做博士后研究，现主要从事代数几何及算术代数几何的研究工作。

邀请人： 吕鑫