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Abstract Zhang

Formality conjecture and moduli spaces of sheaves on K3 surfaces

The formality conjecture on K3 surfaces, formulated by Kaledin and Lehn, states that the differential graded algebra RHom(F,F) is formal for any sheaf F polystable with respect to an ample line bundle on a complex K3 surface. In this talk, I will explain how to combine techniques from hyperkähler geometry, dg categories, Fourier-Mukai transforms and wall-crossing to prove this conjecture and its generalization to derived objects. Based on joint work with Nero Budur.