Window shifts and spherical (co)twists

Will Donovan (University of Edinburgh)

Monday 30th January, 2012 15:00-16:00 416


Interest in derived categories has been driven in recent years by connections with theoretical physics and birational geometry. For instance, given a suitable variety X we can perform a flop (a particular sort of birational map) to a new variety X': in this setting we hope to find that the derived categories of X and X' are equivalent, however this is hard to prove in general. We will describe in particular examples how the desired equivalence can be seen in terms of brane transport between related string theories, by choosing a "window" of branes. We can then produce derived automorphisms of X by "window shifting": we explain this construction and describe the results in terms of spherical (co)twists. (Joint work with Ed Segal.)

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