Representations of p-adic Groups Conference: Schedule

All talks will be held in the Anatomy lecture theatre, K6.29 in the King's Building at King's College London. Enter King's through the Strand Building. Tea/coffee breaks and the reception will be in the Anatomy Museum, right next to the lecture theatre.

Monday, September 2nd

1pm Arrival and welcome

1:30pm Dipendra Prasad

2:30pm Tea and coffee

3pm Justin Trias

4pm Jack Shotton

5:30pm Reception and poster session

Tuesday, September 3rd

9:30am Jessica Fintzen

10:30am Tea and coffee

11am Freydoon Shahidi

2pm Paul Broussous

3pm Tea and coffee

3:30pm Talk about Colin's work by Guy Henniart, Phil Kutzko, and Shaun Stevens

5:15pm Memories of Colin

6:30pm Optional dinner at Paro (see the main conference page for details)

Wednesday, September 4th

9:30am Rob Kurinczuk

10:30am Tea and coffee

11am Anna Szumowicz

12pm Marie-France Vignéras

Talk Titles and Abstracts

Paul Broussous, "Distinction of Iwahori-spherical representations"

Let G(F)\G(E) be a Galois symmetric space, where G is a simply connected semisimple algebraic group defined and split over a non-archimedean local field F. We fix an Iwahori subgroup I of G(E), that is a minimal parahoric subgroup, and denote by H the corresponding Hecke-Iwahori algebra.  According to Borel and Casselman, the category of complex smooth representations of G(E) that are Iwahori spherical (i.e. generated by the subspace of I-fixed vectors)  is equivalent to the category of left H-modules. We show that it is possible to study Iwahori-spherical representations of G(E) that are distinguished by G(F) via their corresponding modules over H. The main tool is a good understanding of the orbits of G(F) in the Bruhat-Tits building of G(E).

Jessica Fintzen, "Structure of Hecke algebras arising from types, and reduction to depth-zero"

We show that one can reduce a lot of problems about the (category of) smooth complex representations of p-adic groups to problems about representations of finite groups of Lie type, where answers might already be known or are easier to achieve. More precisely, the category of representations of p-adic groups decomposes into subcategories, called Bernstein blocks. Combining work of Bushnell and Kutzko, Kim and Yu, and the speaker, under minor tameness assumptions, each of these blocks is equivalent to the category of modules over a Hecke algebra attached to a type. In this talk we provide a description of the structure of these Hecke algebras and show that each of them is isomorphic to the Hecke algebra of a depth-zero Bernstein block. This is based on two recent preprints with Adler, Mishra and Ohara.

Robert Kurinczuk, "Block decompositions for p-adic classical groups"

Let G be a p-adic classical group with p odd, and R an integral domain and Z[1/p,μ_{p^∞}]-algebra.  The category of smooth representations on R-modules decomposes into a product of indecomposable subcategories called R-blocks.  In this talk, I will introduce a graph whose connected components index the R-blocks and associate a finitely generated projective generator to each R-block.  This is joint work with Helm, Skodlerack, and Stevens.

Dipendra Prasad, "Symplectic periods of GL(2n) representations:  the case of inner forms"

For F a local field, representations of GL(2n,F) distinguished by Sp(2n,F) (i.e., one carrying an Sp(2n,F)-invariant linear form) were classified by Offen-Sayag almost two decades ago. This lecture will review some general results about the distinction problem, and then discuss what's known about this problem for the case of Sp(n,D) contained inside GL(n,D), where D is a quaternion algebra. It leads to questions about the global Jacquet-Langlands correspondence which seem unknown (to me).

Freydoon Shahidi, "Local Langlands Correspondence and L-functions"

After discussing the local Langlands correspondence (LLC) briefly, we define a global motivic Artin L-function attached to any cuspidal automorphic representation of a reductive group over a number field and any finite-dimensional representation of its L-group with the hope that understanding the automorphic side may tell us something about the Artin side. We then discuss the possible general approaches to understanding the automorphic side, including a discussion of degenerate models of Moeglin-Waldspurger for any irreducible admissible representation, connecting them to the wavefront set (WFS) of the representation. We conclude by presenting a conjecture of A. Hazeltine, B. Liu, H-C. Lo and I on understanding WFS for any irreducible admissible representation, and discuss WFS of Arthur packets and corresponding conjectures, e.g., Jiang's conjecture and the enhanced Shahidi's conjecture for classical groups.

Jack Shotton, "Endomorphism algebras of Gelfand-Graev representations"

Let G be a reductive group over a finite field F of characteristic p. I will present work with Tzu-Jan Li in which we determine the endomorphism algebra of the Gelfand-Graev representation of the finite group G(F) where the coefficients are taken to be l-adic integers, for l a good prime of G distinct from p. Our result can be viewed as a finite-field analogue of the local Langlands correspondence in families.

Anna Szumowicz, "Bounding Harish-Chandra characters"

Let G be a connected reductive algebraic group over a p-adic local field F. We study the asymptotic behaviour of the trace characters θ_π evaluated at a regular semisimple element of G(F) as π varies among supercuspidal representations of G(F). Kim, Shin and Templier conjectured that θ_π(γ)/deg(π) tends to 0 when π runs over irreducible supercuspidal representations of G(F) whose central character is unitary and the formal degree of π tends to infinity. I will sketch the proof that for G semisimple the trace character is uniformly bounded on γ under the assumption, which is believed to hold in general, that all irreducible supercuspidal representations of G(F) are compactly induced from an open compact modulo center subgroup. If time allows I could also discuss progress on optimizing the bound. 

Justin Trias, "l-modular theta correspondence"

The local theta correspondence over a non-Archimedean local field (of residual characteristic p) claims a bijection between (subsets of) irreducible complex representations of two reductive groups forming a dual pair in a symplectic group. I will explain how to generalise the framework of this statement to l-modular representations i.e. when the coefficient field has characteristic l different from p. This leads to a modular theta correspondence provided l is large enough compared to the size of the groups at stake.

Marie-France Vignéras, "Representations of the local non-archimedean group SL(2)"

The study of the complex smooth  representations of the local non-archimedean special linear group SL(2,F) has a long history, and  Bushnell studied with Kutzko the admissible dual of SL(n,F). The study of the  modular  representations  started only recently with the work of Peiyi Cui. With Guy Henniart, we investigated thoroughly the irreducible representations of SL(2,F) over an algebraically closed field R assuming only   that  the characteristic char(R) of R is not  the residual characteristic p of F. There is a  Langlands correspondence, which is enhanced if char(R) is not 2. Near the identity, any irreducible non-trivial representation is isomorphic modulo a  finite dimensional representation, to a sum of elements in an L-packet of size 4.

Posters

Tom Adams, "Realising The Smooth Representations of GL2(O_F) Using p-adic Geometric Methods"

Jacksyn Bakeberg, "Excursion functions on SL(2)"

Rose Berry, "The Derived Unipotent Block of GL(n) as Complexes over a dg-Schur Algebra"

Elena Collacciani, "A reduction over finite fields of the Tame Local Langlands correspondence for the General Linear Group"

Stefan Dawydiak, "Lusztig's asymptotic Hecke algebra and p-adic groups"

Vincenzo Di Bartolo, "Augmented Iwasawa algebras in the Langlands program"

Mick Gielen, "Canonical dimensions for depth-zero supercuspidal representations of p-adic groups"

Johannes Girsch, "Degenerate representations of GL(n,F)"

Alexandros Groutides, "Integral aspects of Rankin-Selberg periods and applications"

Constantinos Papachristoforou, "Explicit depth-zero block decompositions for G2"

Chuan Qin, "Involution for the representations of Hecke algebras"

James Taylor, "Equivariant Vector Bundles with Connection on Drinfeld Symmetric Spaces"

Ekta Tiwari, "Branching rules for irreducible supercuspidal representations of unramified U(1,1)"

Zhixiang Wu, "Bernstein-Zelevinsky duality for locally analytic principal series representations"

Jiandi Zou, "Simple type theory for metaplectic covers of GL(r) and applications"

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