# 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:

- pages 46–55 of my book with Couveignes:
http://www.math.u-bordeaux1.fr/~jcouveig/book.htm
- pages 7–21 of Jean-Baptiste Nortier's unfinished thesis:
http://pub.math.leidenuniv.nl/~edixhovensj/talks/2001/crmedix.pdf
- 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.

## Further information

For further information, please contact one of the organizers. (Contact details are on their homepages.)