The Geometric Langlands Conjecture and Non-Abelian Hodge Theory - Lecture 1

Explore the first lecture on the Geometric Langlands conjecture and non-abelian Hodge theory, delivered by Ron Donagi as part of the Quantum Fields, Geometry and Representation Theory program. Delve into the intricate world of mathematical physics, covering topics such as the Langlands program, surfaces, local systems, and various versions of the Geometric Langlands Conjecture (GLC). Learn about abelian and non-abelian cases, proofs, reformulations, and the Hecke correspondence. Gain insights into randified and compactified versions of the GLC, and prepare for future lectures in this series. Engage with a Q&A session at the end to deepen your understanding of these complex mathematical concepts and their connections to theoretical physics.

Quantum Fields, Geometry and Representation Theory
The Geometric Langlands conjecture and non-abelian Hodge theory Lecture 1
Langlands program
GLC
Surfaces
G any group: G local system on x
Abelian GLC
Proof
Proof 2
Reformulation
GLC - Correspondence
Heck correspondence
GLC - One Version Generated language
Other versions
Randified abelian GLC
Compactified
Conjecture
Next class
Q&A