Abstract: This semester the RTG seminar will focus on the Kudla program. I will give an introduction to this program, which seeks to understand the relation between arithmetic intersection theory on Shimura varieties and L-functions. While there are close connections to the body of conjectures relating algebraic cycles to L-functions (such as the Bloch-Beilinson conjectures), the Kudla program has some additional mysterious features. For instance, in certain cases, it involves not the leading Taylor coefficient of an L-function but rather the subleading term. Other topics that it is related to include the theory of the theta correspondence, Kudla-Millson theory and Borcherds lifts. This talk will explain some of the history of the subject and how some of these ideas tie together.

The entire list of talks for the semester can be found at this link: https://umrep.github.io/

All are welcome to attend. If you are interested in giving a talk, please send me an email!