# Equivalences from geometric $sl_2$ actions

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Sabin Cautis, Rice University
Fine Hall 322

We explain how $sl_2$ 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 via correspondences on the cotangent bundles of Grassmannians which generalizes the basic Mukai flop. 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. (joint with Joel Kamnitzer and Anthony Licata)