On the Kudla-Rapoport Conjecture - Chao Li

Explore the Kudla-Rapoport conjecture in this comprehensive lecture from the Joint IAS/Princeton University Number Theory Seminar. Delve into Hurwitz class numbers and their relations, examining a geometric proof of Hurwitz's formula and its reinterpretation. Investigate the connection to Eisenstein series of genus 2 and the Gross-Keating formula. Learn about the L-functions associated with the Kudla-Rapoport conjecture and gain insights into the current state of knowledge surrounding this mathematical problem. Examine the unitary Rapoport-Zink space and its geometry, as well as arithmetic intersection numbers. Understand the proof strategy involving induction, the uncertainty principle, and decomposition techniques. This in-depth talk by Chao Li from Columbia University offers a thorough exploration of this complex mathematical topic.

Syllabus

Intro
Hurwitz class numbers
Hurwitz class number relations Example
A geometric prool of Hurwitz's formula
Reinterpretation of Hurwitz's formula
Relation with Eisenstein series of genus 2
Gross-Keating formula
Remarks on KR conjecture: L-functions
Summary
What is known about KR conjecture?
The unitary Rapoport-Zink space
Geometry of
Arithmetic intersection number IntL
Proof strategy induction on
Proof strategy apply the uncertainty principle
Proof strategy: decomposition