We will have a one-day seminar series on 2nd August, 2024 to celebrate Paul Nelson's 40th birthday.
Venue: Queen Mary University of London, School of Mathematical Sciences, room: MB-503.
We will have a one-day seminar series on 2nd August, 2024 to celebrate Paul Nelson's 40th birthday.
Venue: Queen Mary University of London, School of Mathematical Sciences, room: MB-503.
9:00-9:50: Nina Zubrilina (Princeton University)
Murmuration
Birds are modular.
9:50-10:10: Coffee break
10:10-11:00: Ian Petrow (University College London)
Generalized PGL(2) Petersson/Bruggeman/Kuznetsov formulas
I will present hypotheses for test function pairs f <-> pi(f) for the pre-trace formula on PGL(2) that produce Fourier trace formulas closely resembling the classical Petersson/Bruggeman/Kuznetsov formulas upon unipotent integration. Then, I will discuss as an example the case that pi(f) selects a single (up to unramified quadratic twist) supercuspidal representation, extending work of Yueke Hu. We use the minimal vector theory of Hu, Nelson, and Saha, to produce our test function pairs. This work is joint with Yueke Hu and Matthew P. Young.
11:00-11:50: Yannis Petridis (University College London)
Counting, equidistribution, and refinements
I will discuss how counting orbits in hyperbolic spaces lead to interesting number theoretic problems. The counting problems (and the associated equidistribution) can be studied with various methods: automorphic form techniques, originating in the work of H. Huber and studied extensively by A. Good, Chatzakos, Cherubini, Lekkas, Risager, Voskou, ergodic theory, and, for special cases, using direct algebraic number theory and Weyl sums. My collaborator in this project is M. Risager.
12:00-13:30: Lunch
13:30-14:20: Sumit Kumar (Aarhus University)
Subconvexity for Rankin-Selberg L-functions
Abstract: In this talk, I will discuss the subconvexity problem for the Rankin-Selberg L-functions. This problem is resolved in a breakthrough work by Michel-Venkatesh with the period integral approach. We use the delta-symbol approach to give another proof of the Michel-Venkatesh theorem over Q. Ongoing project joint with Aggarwal, Kwan, J. Li, Leung and M. Young.
14:20-15:10: Soumendra Ganguly (Aarhus University)
Hybrid subconvex bounds for selfdual GL(3) L-functions via GL3 × GL2 ↭ GL4 × GL1 spectral reciprocity.
Abstract: We prove a spectral reciprocity formula which relates a GL2 moment of GL3 × GL2 Rankin–Selberg L-functions to a GL1 moment of GL4 × GL1 Rankin–Selberg L-functions. We prove hybrid subconvex bounds for selfdual GL3 L-functions twisted by primitive Dirichlet characters of arbitrary conductor q simultaneously in the q and t aspects. We additionally prove analogous hybrid subconvex bounds for central values of GL3 × GL2 Rankin–Selberg L-functions.
15:10-15:30: Coffee Break
15:30-16:20: Kevin Kwan (University College London)
Variations on a theme after Dirichlet
The main goal of this talk is to illustrate, through analogies and concrete examples, how some of Dirichlet's (and Nelson’s) ideas can be used to study L-functions.
16:30-17:00: Paul Nelson (Aarhus University)
Pushing a boulder too close to the sun
18:00: Dinner