Laumon spaces and representation theory (joint work with B. Feigin, M. Finkelberg and A. Negut)

Laumon spaces are certain smooth closures of the moduli spaces of maps from the projective line to the flag variety. We construct the action of the Yangian of $sl_n$ in the localized equivariant cohomology of Laumon spaces by certain natural correspondences. This gives a natural representation-theoretic explanation of the appearance of Toda system in quantum cohomology of flag varieties.