Edward Witten: Mirror Symmetry & Geometric Langlands [2012] 

2012 FIELDS MEDAL SYMPOSIUM
Thursday, October 18
Geometric Langlands Program and Mathematical Physics
1.30am-2.30pm
Edward Witten, Institute for Advanced Study, Princeton
"Superconformal Field Theory And The Universal Kernel of Geometric Langlands"
The universal kernel of geometric Langlands for a group G can be understood as a three-dimensional superconformal field theory T(G) with OSp(4|4) symmetry. Arthur's SL_2 is a subgroup of this OSp(4|4) and mirror symmetry acts via an outer automorphism of OSp(4|4). As an application, we will explain a quantum field theorist's view of " geometric Eisenstein series.'' T(G) is the prototype of a family of three-dimensional superconformal field theories which are basic examples of three-dimensional mirror symmetry -- or symplectic duality -- and also play a role in geometric Langlands.
Video taken from:
www.fields.uto...