We are happy to announce that Zhiwei Yun will be giving a series of lectures in algebraic geometry this spring. The title and abstract for the entire series is:
Geometry in orbital integrals and beyond:The Gross-Zagier formula is an identity between the first derivative of the L-function of an elliptic curve at s=1 and an intersection number. In joint work with Wei Zhang, we give a generalization of the Gross-Zagier formula to higher derivatives of the L-function for elliptic curves over function fields. In this series of lectures, I will discuss some geometric ideas involved in the proof of this formula which originated from the study of orbital integrals. |
The series will begin with a pretalk: Shuyang Cheng will give an introduction to the geometry of orbital integrals on Friday, March 17 between 3:00pm and 5:00pm in 1096 East Hall.
The schedule for this lecture series, as well as titles and abstracts for individual talks, is displayed below. Note that Zhiwei's first lecture will be a colloquium talk intended for a general mathematical audience. All lectures will take place in East Hall.
| Day | Time | Room | Title |
|---|---|---|---|
| Tuesday, March 21
(Colloquium talk) |
3:10 - 4:00 | 1360 EH | I will talk about my joint work with Wei Zhang on generalizing the Gross-Zagier and Waldspurger formulae to higher derivatives of L-functions for function fields. |
| Wednesday, March 22 | 4:10 - 5:30 | 4096 EH | Orbital integrals are important quantities in the theory of automorphic forms, and they usually appear when one applies trace formula. I will review relevant background of the subject and mention some examples. |
| Thursday, March 23 | 4:10 - 5:30 | 1866 EH | I will talk in more details about the geometry of orbital integrals that appear in the theorem mentioned in Lecture 1. |
| Friday, March 24 | 4:10 - 5:30 | 2866 EH | In the last lecture, I will talk about some ingredients in the proof of the theorem beyond orbital integrals. I will also mention our recent work with Wei Zhang which extends our previous theorem by allowing ramifications. |
This is our fifteenth Spring Lecture Series in Algebraic Geometry. Previous speakers have been (in reverse chronological order): Arnaud Beauville, Jacob Lurie, Peter Scholze, Manjul Bhargava, Richard Thomas, Bjorn Poonen, Daniel Huybrechts, Marc Levine, Mihnea Popa and Giuseppe Pareschi, Ravi Vakil, Shigeru Mukai, Paul Biran, and Burt Totaro.