RTF reading seminar Fall 2024 - Spring 2025

SYNOPSIS

The seminar will meet Wednesday 3:30-5:00PM+ in Van Vleck B211 .

The goal of this two-semester long semiar is to have a understand the sprits the relative trace formula and their applications. In the first semester, we will review the automorphic representations, study the regular trace formula, and prove the Jacquet-Langlands correspondence. In the second semester, we will go into Jacquet's proof of Waldspurger formula, then some further topics.

To receive the messages, please subscribe our google group by sending any message to 2024-2025_rtf-reading-seminar+subscribe@g-groups.wisc.edu. To get credits, please enroll Math941 SEM004, and give a talk in the seminar. You are encouraged to give more than one talks since we don't have enough speakers.

Schedule

2024 Fall Wednesday 3:30-5:00PM+, Van Vleck B211
Sept. 11 Zhiyu Zhang Introduction to the relative trace formula.
Sept. 18 Ryan Tamura Automorphic representations for \(\mathrm{GL}_2\).
Sept. 25 Phillip Harris Representation of \(\mathrm{GL}_2(\mathbb{R})\).
Oct. 2 Chenghuang Chen Representations of \(\mathrm{GL}_2(\mathbb{Q}_p)\).
Oct. 9 Alejo Salvatore L-groups, L-functions, functoriality.
Oct. 16 Phillip Harris Trace formula for compact quotient.
Oct. 23 Simon Marshall Trace formula for non-compact quotient I.
Oct. 30 (Maybe still) Simon Marshall Trace formula for non-compact quotient II.
Nov. 6 TBD Trace formula for adelic quotient.
Nov. 13 TBD Jacquet-Langlands correspondence I.
Nov. 20 TBD Jacquet-Langlands correspondence II.
Nov. 27 Thanksgiving recess
Dec. 4 TBD Tanya Khovanova's recent work
2025 Spring
TBD TBD Hecke periods et al.
TBD TBD Waldspurger formula and applications.
TBD TBD Jacquet's proof of Waldspurger formula I.
TBD TBD Jacquet's proof of Waldspurger formula II.
TBD TBD Jacquet's proof of Waldspurger formula III.
TBD TBD Jacquet's proof of Waldspurger formula IV.
TBD TBD Jacquet's proof of Waldspurger formula V.
TBD TBD Further topics I.
TBD TBD Further topics II.
TBD TBD Further topics III.
TBD TBD Further topics IV.

References

Automorphic representations Regular trace formula and Jacquet-Langlands correspondence Period integral formula Waldspurger formula Additional references

Outline

Here are some topics we want to pursue in the seminar.

Part 0: Introduction

Abstract: In this talk, we will talk about relative trace formulas, which are equalities between period integrals (the spectral side) and relative orbital integrals (the geometric side) as distributions on compactly supported adelic functions for the reductive group \(G\). We will explain the general principle, and then focus on examples related to Gan-Gross-Prasad conjecture and Rankin-Selberg periods for \(G=GL_n \times GL_m\).

Part 1: Overview of Automorphic representations

Part 2: Regular trace formula and Jacquet-Langlands

Part 3: Introduction to period integral formulas and applications.

Part 4: Jacquet’s proof of Waldspurger formula

Give an overview of those period integral formulas, and mention some application. Then maybe Simon could say something about the philosophy behind those formulas.

Part 5: Further topics

This seminar is organized by Jiaqi Hou, Yu LUO and Simon Marshall. This page is took from Brian Lawrence's reading seminar