Time: August 16, Friday, 16:00-17:00

Venue: Lecture Hall

Speaker: Wei Zhang ( MIT )

Abstract: Zeta functions or more generally L-functions arise naturally in number theory and arithmetic geometry. They are meromorphic functions in one complex variable with functional equations. The leading terms of of their Taylor expansion  (at the central or near central points of the function equations) encode deep arithmetic geometric information, as the class number formula, the conjecture of Birch-Swnnerton-Dyer, and their generalizations suggest. However, there are very few instances where the sub-leading term (the term after the leading term in Taylor expansion) meets arithmetic geometry, including the Kronecker limit formula and Colmez’s conjecture We will propose a  new conjecture regarding sub-leading terms of certain L-functions and Faltings heights, and survey some related results (based on work in progress with Ryan Chen and Weixiao Lu).