Feb 13  Tue  Luis Santiago Palacios (Bordeaux)  Number Theory seminar  
13:00  Geometry of the Bianchi eigenvariety at noncuspidal 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 padic 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 noncuspidal point. This is a joint work in progress with Daniel Barrera (Universidad de Santiago de Chile). 



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 padic groups. The LLC is divided into two parts: first, there is the tame or depthzero part, where much is known and proofs tend to be uniform for all residue characteristics p. Then there is the positivedepth (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. 



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 LoefflerSkinnerZerbes, we will introduce certain unramified Hecke modules containing lattices with deep integral properties. We'll see how this approach recovers a GrossPrasad 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. 



Mar 5  Tue  Lewis M Combes  Number Theory seminar  
13:00  
Hicks Seminar Room J11 / Google Meet  


Mar 12  Tue  Andrea Dotto (Cambridge)  Number Theory seminar  
13:00  
Hicks Seminar Room J11 / Google Meet  


Apr 30  Tue  Bence Hevesi (Kings College London)  Number Theory seminar  
13:00  
Hicks Seminar Room J11 / Google Meet  


May 7  Tue  Jay Taylor (Manchester)  Number Theory seminar  
13:00  
Hicks Seminar Room J11 / Google Meet  


May 21  Tue  Owen Patashnick (Kings College London)  Number Theory seminar  
13:00  
Hicks Seminar Room J11 / Google Meet  

