Analytic Number Theory seminar

Introduction

This seminar will cover various modern papers in analytic number theory. We will study the paper by Nelson-Venkatesh where they develop a "relative" orbit method, which concerns a pair of representations from two different reductive groups. It has various applications to Number Theory - the supnorm problem, Sarnak's density hypothesis and the subconvexity bound of automorphic forms. We will also look at more explicit methods in Analytic number theory.

References

Schedule

Organisers: Aditya Ghosh, Alan Zhao, Austin Lei

Date: Fall 2026

Time: 4:30-5:30 pm

Location: Room 528, Mathematics Hall

Topics Covered

Serial No. Date Speaker Title and Abstract Notes
1 15 Sept Aditya Ghosh Relative Orbit Method: Part I We discuss the orbit method from Lie theory and various applications to number theory. We give a brief introduction to the relative trace formula and period formulae.
2 22 Sept Aditya Ghosh Relative Orbit Method: Part II We will continue our discussion from last week. Using a "relative" Kirillov orbit formula, we develop a good choice of test vectors used to solve subconvexity.
3 29 Sept Alan Zhao Spectral Multipliers in the Kuznetsov Trace Formula We extend the class of test functions available in the Kuznetsov trace formula and use it to give a simplified criterion to cancellation in the error term of the hyperbolic circle problem.
4 6 Oct TBD (H)

Contact Us

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

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

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