École polytechnique – Centre de Mathématiques Laurent Schwartz

Konstantin JAKOB (Univ. Duisburg-Essen, Allemagne)

10h00-10h45 : Rigid Local Systems and the Geometric Langlands Correspondence

Résumé: Classically, rigid local systems arise as solution sheaves of certain regular singular differential equations in the complex domain. They have been studied in depth by N. Katz who devised a way of constructing these local systems from systems of rank one by means of a convolution operation. However, this construction has several disadvantages. For example it only works for GL_n-local systems. In this talk I will report on work in progress (joint with Z. Yun) on another approach to construct rigid local systems for more general reductive groups via the geometric Langlands correspondence based on ideas of Heinloth, Ngô & Yun. 

11h15-12h00 : A Rigid Automorphic Representation for G_2

Résumé : In this talk I will explain how to construct a rigid automorphic representation with explicit local factors for the simple algebraic group G_2. This automorphic representation is the potential counterpart of a rigid connection with differential Galois group G_2 constructed in my thesis. The construction is mostly based on combinatorics of a certain adelic double quotient related to the moduli of G_2-bundles with level structure. This is joint work with Z. Yun.