AbstractIn my talk, I will report on recent joint work with I. Biswas, S. Dumitrescu and S. Heller showing the existence of holomorphic maps from a compact Riemann surface of genus g>1 into a quotient of SL(2,C) modulo a cocompact lattice which is generically injective. This gives an affirmative answer to a question raised by Huckleberry and Winkelmann and by Ghys. The proof uses ideas from har...
Abstract:Given a singularity with a crepant resolution, a symmetry of the derived category of coherent sheaves on the resolution may often be constructed. I discuss work in progress on general constructions of such symmetries for hypersurface singularities. This builds on previous results with Segal, and is inspired by work of Bodzenta-Bondal