Speaker: Junqing Qian（Union College）
Time: 09:00-10:00, Nov 16, 2022
Room: Tencent Meeting: 474-848-863, no password
In this talk, we will talk about a connection between two subjects in two different fields, i.e., modular functions in number theory and metrics in differential geometry. The problem of deriving the asymptotic expansion of the complete Kahler-Einstein (KE) metric on quasi-projective manifolds was proposed by Yau in the late 70s. People have worked on it by using PDE techniques. However, such analytic approaches lose control after a certain order due to a lack of global information. The speaker discovered in her thesis that a connection between modular functions and metrics could ultimately settle the asymptotics of the KE metric in several nontrivial cases. The root of this connection traces back to the classical uniformization theorem from the early 19th century. We will introduce background knowledge from each field and some theorems that build the "bridge". In the end, we will discuss some open problems if time permits.
