Brief description about the workshop:
The workshop will survey topics from a broad range of areas related to L-functions, automorphic forms and automorphic representations with emphasis on the Langlands-Shahidi method and the theory of integral representations for L-functions. The workshop will cover some preliminary material on Tate’s thesis and classical modular forms as well as the necessary background from the representation theory of p-adic groups and Eisenstein series. The material will be  at a level meant for more advanced graduate students as well as postdoctoral fellows working in areas related to L-functions and the Langlands programme. The aim of the workshop will be to summarise the more recent developments in the area of L-functions so as to equip the participants with some of the tools necessary to follow current developments.

1) Preliminaries: Review of adèles, idèles, strong approximation and Tate’s thesis. Classical modular forms to representation theory. Hekce operators and adelisation.

2) The representations of GL _n over a local field: Admissible representations, Hecke algebra modules, the Satake isomorphism, Parabolic induction, supercuspidal representations, generic representations and Whittaker models. Representations of real groups.

3) The global theory ofr GL _n : Eisenstein series relevant to the integral and Langlands-Shahdi method, the spectral decomposition of L ² (Γ\G), cusp forms, the adelic fourier expansion, L-functions as Mellin-transforms.

4) L-functions: The Langlands-Shahidi method, integral representations (for GL _n × GL _m ), converse theorems.

5) Special topics: Special Values of L-functions, Subconvexity and related questions, random matrix theory, zero-free regions.

Speakers

 Schedule