# Local Langlands Microsymposium

We are organizing a Microsymposium on the Local Langlands correspondence at Radboud University in Nijmegen on January 27th, 2015 from 11.30 to 17.30. There will be talks by Bas Edixhoven, Santosh Nadimpalli and Maarten Solleveld. This microsymposium is the conclusion of our local seminar on Local Langlands for $\mathrm{GL}_{2}$.

## Organizational details

Organizers
Johan Commelin and Milan Lopuhaä
Location
HG03.054 (Huygensgebouw, RU, Nijmegen)
Time
11.30 – 17.30 (27/01/2015)

## Schedule

 11.30 – 12.30 Maarten Solleveld 12.30 – 13.30 Lunch 13.30 – 14.30 Santosh Nadimpalli 14.30 – 15.00 Break 15.00 – 16.00 Bas Edixhoven 16.00 – 16.30 Break 16.30 – 17.30 Bas Edixhoven

## Abstracts

Bas Edixhoven (Leiden) — Modular forms, Galois representations, and Global Langlands for $\mathrm{GL}_2$ over the rationals.

I will explain how Galois representations arise from modular curves, modular forms and Hecke algebras. Then I will explain how this is related to representation theory of $\mathrm{GL}_2$ of the finite adeles of $\mathbb{Q}$. No algebraic geometry and knowledge of etale cohomology will be required; complex manifolds and sheaf cohomology should be sufficient.

References:

1. pages 46–55 of my book with Couveignes: http://www.math.u-bordeaux1.fr/~jcouveig/book.htm
2. pages 7–21 of Jean-Baptiste Nortier's unfinished thesis: http://pub.math.leidenuniv.nl/~edixhovensj/talks/2001/crmedix.pdf
3. http://pub.math.leidenuniv.nl/~edixhovensj/talks/2007/ICTP-Trieste.pdf
Santosh Nadimpalli (Leiden) — Representation theory of $\mathrm{GL}_n$ over non-archimedean local fields.
I will talk about the outline of the construction of the dual of the $p$-adic $\mathrm{GL}_n$. We will discuss the theory of Bernstein and Zelevinsky and the links with the local Langlands correspondence. We will also discuss the construction of super-cuspidal representation of $\mathrm{GL}_n$ due to Bushnell–Kutzko.
Maarten Solleveld (Nijmegen) — The local Langlands correspondence for principal series representations.

I will report on joint work with Anne-Marie Aubert, Paul Baum and Roger Plymen.

Let $G$ be a split reductive group over a local non-archimedean field. We show that there exists a local Langlands correspondence for irreducible $G$-representations in the principal series. This correspondence is functorial and can be made bijective (i.e. it includes a parametrization of $L$-packets) by enhancing Langlands parameters.

If time permits, I will also discuss how these issues relate to the ABPS conjecture.

## Venue

The lectures are given in the Huygens Building on the third floor, room HG03.054. Address of the Huyghens Building: Heyendaalseweg 135, Nijmegen. The Huygens building is approximately 250 meters from train station Nijmegen Heyendaal. From Nijmegen central station it can also be reached by taking bus number 10, which takes only 5 minutes to the University. (Recommended stop: Huygensgebouw.) See also the map of the campus.