Professor Dr. Roman Fedorov
University of Pittsburgh and MPIM Bonn
Dienstag, 7. November 2023
Raum 2004 (L1)
über das Thema:
|The talk will be devoted to one of the least developed corners of the geometric Langlands program. Consider a complex smooth projective curve (a.k.a. a compact Riemann surface). For many decades, people have been studying the moduli space of vector bundles on such curves. However, as was discovered by Hitchin in the end of XXth century, the cotangent bundle of this moduli space is a more fundamental object. This cotangent bundle, known as the phase space of the Hitchin system has lots of interesting structures and is related to many areas of mathematics. The global Langlands duality for Hitchin systems is a conjectural auto-equivalence of this phase space. Roughly speaking, this means that the points of this cotangent bundle parameterize certain objects on itself (precisely, the generalized line bundles on the Hitchin fibers). In the simplest case, this reduces to the statement that the line bundles on an elliptic curve are parameterized by the elliptic curve itself. I will recall the notion of a Hitchin system in some detail and will briefly explain the statement of the duality and the current state of knowledge. Then I will focus on the local duality, where the compact curve X is replaced by a formal disc. I will assume very little previous knowledge of algebraic geometry.
|Hierzu ergeht herzliche Einladung.
|Prof. Dr. Maxim Smirnov
Kaffee, Tee und Gebäck eine halbe Stunde vor Vortragsbeginn im Raum 2006 (L1).