Elias Sink (Harvard): Semiorthogonal decompositions and the Hecke correspondence

The philosophy of noncommutative algebraic geometry is that one should regard semiorthogonal components in derived categories of smooth varieties as “noncommutative spaces.” In particular, Van den Bergh and Kuznetsov have introduced notions of a noncommutative resolution of singularities. We construct full semiorthogonal decompositions of (twisted) noncommutative resolutions of the moduli space of semistable rank 2 vector bundles of trivial determinant on a curve of genus at least 2. These are related to the Tevelev-Torres semiorthogonal decomposition of the moduli space of stable rank 2 bundles of fixed odd determinant by a mutation on the Hecke correspondence. This is joint work with Jenia Tevelev.