2017
May
29

# NT&AG: Nicolas Templier (Cornell University), "Mirror symmetry for minuscule flag varieties"

2:00pm to 3:00pm

## Location:

Ros70A

We prove cases of Rietsch mirror conjecture that the quantum
connection for projective homogeneous varieties is isomorphic to the
pushforward D-module attached to Berenstein-Kazhdan geometric crystals.
The idea is to recognize the quantum connection as Galois and the
geometric crystal as automorphic. In particular we link the purity of
Berenstein-Kazhdan crystals to the Ramanujan property of certain Hecke
eigensheaves.
The isomorphism of D-modules comes from global rigidity results where a
Hecke eigenform is determined by its local ramification. We reveal