Langlands Program and Applications

Abstract: The goal of this general audience talk is to introduce the L-function attached to a projective variety and state some of its expected properties. A way to prove such properties is to relate the L-function to objects of a more analytic nature (namely automorphic forms). During the talk we will study some baby examples of the correspondence, and state some recent results (as well as some open problems). At last we will explain how the theory is well suited for the study of solutions to Diophantine equations (we will include a 5 minutes proof of Fermat's last theorem).

mathematical physicsalgebraic geometryalgebraic topologydifferential geometryrepresentation theorysymplectic geometry

Audience: researchers in the topic

Geometry and Physics @ Lisbon