Organisers: Aditya Ghosh, Alan Zhao, Austin Lei
Date: Spring 2026
Time: 4:30 PM - 5:30 PM
Location: Room 528, Mathematics Hall
| 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 | Kloosterman Sums on $GSp_4$. In this talk, we will introduce the density hypothesis on $GSp_4$ and introduce prerequisites for understanding the proof of “one half” of the problem. | |
| 3 | 10 Feb | Alan Zhao | Kloosterman Sums on $GSp_4$, Part II. We will continue where we left off last time and finish off introducing higher rank Kloosterman sums. Then, we will continue with exposing the proof of a density hypothesis for $GSp_4$. | |
| 4 | 17 Feb | Aditya Ghosh | Supnorm problem for $PGL(2,\mathbb{R})$ We continue with the estimates of integrals of matrix coefficients from last time. Using the $Op(a)$ operator defined earlier, we will find nice test vectors that can be applied to the supnorm problem. | |
| 5 | 24 Feb | Aditya Ghosh | Supnorm problem for $PGL(2,\mathbb{R})$: Part II We establish the Relative Trace formula used in the supnorm problem. Then, we discuss bounds for the geometric side. |
Aditya Ghosh: ag4794 (at) columbia (dot) edu
Alan Zhao: asz2115 (at) columbia (dot) edu
Austin Lei: ayl2158 (at) columbia (dot) edu