Equivalences from geometric sl_2 actions
Sabin Cautis, Rice

We explain how certain sl_2 actions on derived categories of coherent sheaves can be used to construct new derived equivalences. The example I will describe in detail is an sl_2 action on the cotangent bundle of Grassmannians. More generally we can construct an action on the derived category of coherent sheaves on quiver varieties which lifts Nakajima's action on their cohomology. Conjecturially, one should be able to use these equivalences to construct new knot invariants generalizing Khovanov homology.