9:30
- 10:30 Jack Shotton (Durham)
Local
deformation rings and endomorphisms of Gelfand-Graev
representations
I
will describe some results on the structure of moduli spaces of
Galois representations (in the '\ell \neq p' case) at generic
points on a large subset of components of their special fibres.
They will be smooth over a certain ring of invariants. I will
then explain a conjecture that this ring coincides with the
endomorphism ring of an integral Gelfand-Graev representation,
and give some partial results towards it.
Break
11:00
- 12:00 Beth Romano (Oxford)
A
Fourier transform for unipotent representations of p-adic groups
Representations
of finite reductive groups have a rich, well-understood
structure, first explored by Deligne--Lusztig. In joint work
with Anne-Marie Aubert and Dan Ciubotaru, we show a way to lift
some of this structure to representations of p-adic groups. In
particular, we work with the class of unipotent representations
of split p-adic groups, and consider the relation between
Lusztig's nonabelian Fourier transform and a certain involution
we define on the level of p-adic groups. This talk will be an
introduction to these ideas via examples; I will not assume
previous familiarity with these topics.
Lunch
14:00
- 15:00 Emile Okada (Oxford)
The
wavefront set of admissible representations of p-adic groups.
Abstract:
The wavefront set is a powerful invariant which one can attach
to representations of p-adic groups with applications to the
structure of automorphic representations, branching laws, and
Fourier coefficients of automorphic forms. In this talk we will
discuss the basic definitions and properties of the wavefront
set, followed by methods for computing it, and finally if time
permits, some recent advances connecting the wavefront set to
equivariant perverse sheaves on the complex dual group.
Break
15:30
- 16:30 Robert Kurinczuk (Sheffield)
Local
Langlands in families for classical groups
The
conjectural local Langlands correspondence connects
representations of p-adic groups to certain representations of
Galois groups of local fields called Langlands parameters.
In recent joint work with Dat, Helm, and Moss, we have
constructed moduli spaces of Langlands parameters over Z[1/p]
and studied their geometry. We expect this geometry is
reflected in the representation theory of the p-adic
group. Our main conjecture “local Langlands in families”
describes the GIT quotient of the moduli space of Langlands
parameters in terms of the centre of the category of
representations of the p-adic group generalising a theorem of
Helm-Moss for GL(n). I will explain how after inverting
the "non-banal primes" one can prove this conjecture for the
local Langlands correspondences of Arthur and others .
18:00
Dinner