The level-rank duality for nonabelian theta functions.
Spaces of sections of tensor powers of the theta line bundle on moduli
spaces of semistable arbitrary rank bundles on a smooth
curve are subject to a level-rank duality: each space of
sections is geometrically isomorphic to the dual of the space
of sections obtained by interchanging the tensor power (level) of the
theta bundle on the moduli space and the rank of the
bundles that make up the moduli space.
I will describe a proof of this duality, which is the result of joint
work with Dragos Oprea, and draws inspiration from work by Prakash
who established the isomorphism for a generic curve.