Toward the Proof of the Geometric Langlands Conjecture

Sun, 16/03/2014 to Fri, 21/03/2014



Dima Arinkin, University of Wisconsin-Madison
Dennis Gaitsgory, Harvard University
David Kazhdan, The Hebrew University of Jerusalem
Yakov Varshavsky, The Hebrew University of Jerusalem


The idea of this conference is to explain the state of the art in the area of mathematics known as "Geometric Langlands Correspondence".

Geometric Langlands lies on the juncture between several larger fields, and draws upon ideas from each. Number Theory is the birthplace of Langlands Correspondence -- it was conceived by Robert Langlands in the late 1960s as a generalization of the fundamental results in number theory, known as Class Field Theory. Algebraic Geometry is the place that Geometric Langlands inhabits: the main theorems and conjectures are statements formulated within Algebraic Geometry. Representation Theory enters since the geometries that we study are attached to entities within Representation Theory, the latter being reductive groups. Mathematics Physics appears because some of the most crucial constructions are motivated by ideas from Conformal Field Theory. Finally, Algebraic Topology is the language in which we speak: Geometric Langlands lives in the world of "Higher Categories", where basic objects are not sets but what are known as infinity-groupoids. We hope to convey these ideas to the conference participants and endow them with the technical knowledge to be able to take up projects within Geometric Langlands.