Subconvexity, Orbit Method, and Microlocal Analysis

Introduction

We continue the seminar from Fall 2025. Having set up the necessary prerequisites of the Orbit Method and GGP, we now focus on applying them to various period bounds. These encompass the supnorm problem, Sarnak's density hypothesis and the subconvexity bound of automorphic forms.
Notes from fall semester can be found here.

References

Schedule

Organisers: Aditya Ghosh, Alan Zhao, Austin Lei

Date: Spring 2026

Time: 4:30 PM - 5:30 PM

Location: Room 528, Mathematics Hall

Topics Covered

Serial No. Date Speaker Title and Abstract Notes
1 20 Jan Aditya Ghosh Recap of Fall semester seminar. We shall go over the key prerequisites of the Orbit method covered in the last semester. These includes passing from a Lie group representation to the corresponding coadjoint orbit, Kirillov's orbit formula and the construction of bump functions using the orbit method link
2 27 Jan Aditya Ghosh Application of the orbit method to lower bounds of integrals of matrix coefficients. Having set up the prerequisites for the orbit method, we look at how it is used to obtain test functions that give lower bounds of integrals of matrix coefficients. This is used as one of the main components in the proof of subconvexity or the supnorm problem.
2 3 Feb Alan Zhao TBD

Contact Us

Aditya Ghosh: ag4794 (at) columbia (dot) edu

Alan Zhao: asz2115 (at) columbia (dot) edu

Austin Lei: ayl2158 (at) columbia (dot) edu