Geometric structure in the representation theory of p-adic groups

This masterclass will provide an introduction to the Bernstein decomposition of the smooth dual of a reductive p-adic group, and to the recent conjectures of Aubert, Baum, Plymen and Solleveld on the geometric structure of the Bernstein components. The lectures are aimed primarily at PhD-students and post-docs, and will include introductory material on the representation theory of p-adic groups and the local Langlands correspondence.

The lectures will be held at the Department of Mathematical Sciences at the University of Copenhagen, and the event is hosted by the Centre for Symmetry and Deformation.

Lecturers:

Mini-courses will be given by:
Joseph Bernstein (Tel Aviv University) [abs1]
Maarten Solleveld (Radboud University Nijmegen) [abs2]

Additional lectures will be given by:
Paul Baum (Penn State University) [abs3]
Eitan Sayag (Ben-Gurion University of the Negev) [abs4]

The lecture series will be supported by several shorter lectures, covering background material, examples, etc. These will be given by Venketasubramanian C G, Arnab Mitra, Ahmed Moussaoui, Avner Segal and Alexander Yom Din.

Schedule:

Notes, slides, etc:

Notes and slides:
[pdf1] Maarten Solleveld: Introduction to the local Langlands correspondence and the ABPS conjecture (draft notes).
[pdf2] Alexander Yom Din: Background from category theory. (See also these notes: [pdf].)
[pdf5] Avner Segal: L-groups
[pdf6] Ahmed Moussaoui: Local Langlands correspondence and examples of ABPS conjecture.

Problems:
[pdf7] Problem sheet 1 for the Bernstein-Sayag lectures
[soon] Problem sheet 2 for the Bernstein-Sayag lectures
[soon] Problem sheet 3 for the Bernstein-Sayag lectures

Recommended background reading:
[pdf8] Bernstein: Representations of p-adic groups. Lectures by Joseph Bernstein, written by Karl E. Rumelhart. Harvard University. (Fall 1992).
[pdf9] Bernstein, Zelevinsky: Representations of the group GL(n,F), where F is a local non-Archimedean field. Uspekhi Mat. Nauk 10, No.3, 5-70 (1976).
Wedhorn: The Local Langlands Correspondence for GL(n) over p-adic Fields. In School on Automorphic Forms on GL(n) (ed. by L. Göttsche, G. Harder, M.S. Raghunathan), ICTP Lecture Notes 21 (2008), 237 - 320.
[www1] Aubert, Baum, Plymen, Solleveld: Geometric structure and the local Langlands conjecture. arXiv:1211.0180 (2012)

Participants:

[www2] List of participants

Organised by Tyrone Crisp and Job Kuit (Copenhagen).