Seminars this semester


   Series:

 
Feb 13 Tue Luis Santiago Palacios (Bordeaux) Number Theory seminar
13:00 Geometry of the Bianchi eigenvariety at non-cuspidal points
Hicks Seminar Room J11 / Google Meet
  Abstract:
An important tool to study automorphic representations in the framework of the Langlands program, is to produce $p$-adic variation. Such variation is captured geometrically in the study of certain "moduli spaces" of p-adic automorphic forms, called eigenvarieties. In this talk, we first introduce Bianchi modular forms, that is, automorphic forms for $\mathrm{GL}_2$ over an imaginary quadratic field, and then discuss its contribution to the cohomology of the Bianchi threefold. After that, we present the Bianchi eigenvariety and state our result about its geometry at a special non-cuspidal point. This is a joint work in progress with Daniel Barrera (Universidad de Santiago de Chile).
Click here to insert in your Google calendar
 
Feb 20 Tue Beth Romano (Kings College London) Number Theory seminar
13:00 Epipelagic representations in the local Langlands correspondence
Hicks Seminar Room J11 / Google Meet
  Abstract:
The local Langlands correspondence (LLC) is a kaleidoscope of conjectures relating local Galois theory, complex Lie theory, and representations of p-adic groups. The LLC is divided into two parts: first, there is the tame or depth-zero part, where much is known and proofs tend to be uniform for all residue characteristics p. Then there is the positive-depth (or wild) part of the correspondence, where there is much that still needs to be explored. I will talk about recent results that build our understanding of this wild part of the LLC via epipelagic representations and their Langlands parameters. I will not assume background knowledge of the LLC, but will give an introduction to these ideas via examples.
Click here to insert in your Google calendar
 
Feb 27 Tue Alexandros Groutides (Warwick) Number Theory seminar
13:00 On integral structures in smooth $\mathrm{GL}_2$-representations and zeta integrals.
Hicks Seminar Room J11 / Google Meet
  Abstract:
We will discuss recent work on local integral structures in smooth ($\mathrm{GL}_2\times H$)-representations, where $H$ is an unramified maximal torus of $\mathrm{GL}_2$. Inspired by work of Loeffler-Skinner-Zerbes, we will introduce certain unramified Hecke modules containing lattices with deep integral properties. We'll see how this approach recovers a Gross-Prasad type multiplicity one result in this unramified setting and present an integral variant of it with applications to zeta integrals and automorphic modular forms. Finally, we will reformulate and answer a conjecture of Loeffler on integral unramified Hecke operators attached to the lattices mentioned above.
Click here to insert in your Google calendar
 
Mar 5 Tue Lewis M Combes Number Theory seminar
13:00
Hicks Seminar Room J11 / Google Meet
Click here to insert in your Google calendar
 
Mar 12 Tue Andrea Dotto (Cambridge) Number Theory seminar
13:00
Hicks Seminar Room J11 / Google Meet
Click here to insert in your Google calendar
 
Apr 30 Tue Bence Hevesi (Kings College London) Number Theory seminar
13:00
Hicks Seminar Room J11 / Google Meet
Click here to insert in your Google calendar
 
May 7 Tue Jay Taylor (Manchester) Number Theory seminar
13:00
Hicks Seminar Room J11 / Google Meet
Click here to insert in your Google calendar
 
May 21 Tue Owen Patashnick (Kings College London) Number Theory seminar
13:00
Hicks Seminar Room J11 / Google Meet
Click here to insert in your Google calendar