Abstracts

Konstantin Ardakov:

TBA

Gabriel Dospinescu: On some locally analytic representations of $D^*$

I will report on joint work in progress with Benchao Su, whose aim is to recover an irreducible supersingular representation of $\mathrm{GL}_2(\mathbb{Q}_p)$ from the associated representation of $D^*$ by Scholze's functor. I will describe a (conjectural so far) recipe for this, which works for many representations.

Claudius Heyer: On Second Adjointness for mod $p$ Representations

The parabolic induction functor for smooth representations admits the Jacquet functor as a left adjoint. For complex representations it is a deep result of Bernstein, called Second Adjointness, that the Jacquet functor for the opposite parabolic is (up to a twist) also right adjoint to parabolic induction. A similar result is also known for mod $\ell \neq p$ representations, yet for mod $p$ representations the story is a bit more intricate. But due to recent work of Hoff–Meier–Spieß the (derived) right adjoint of parabolic induction is now fairly well understood. In this talk I will explain Second Adjointness for mod $p$ representations; this is joint work with Manuel Hoff, Sarah Meier and Michael Spieß. If time permits, I will also sketch a different approach to Second Adjointness through Hyperbolic Localization; this is ongoing joint work in progress with Lucas Mann and Konrad Zou.

Christine Huyghe: Fourier transform for coadmissible $D$-modules

I will construct a Fourier transform for coadmissible $D$-modules over rigid analytic fiber bundles, and explain some properties of this transformation.

Wiesława Nizioł: Topological Vector Spaces

The category of Banach-Colmez spaces embeds fully into the category of Vector Spaces (pro-étale $\mathbb{Q}_p$-sheaves) as well as into the category of Topological Vector Spaces (enriched topological presheaves). I will discuss this embeddings and the computation of the Ext-groups of Banach-Colmez spaces. This is based on a joint work with Pierre Colmez.

Sascha Orlik: On some non-principal locally analytic representations

In my talk I will construct some locally analytic representations which do not lie in the principal series. Further I will discuss some basic properties of them.