Title: Semiorthogonal decompositions of Quot schemes and applications
Abstract: In this talk, I will give semiorthogonal decompositions (SOD) of derived categories of coherent sheaves on some relative Quot schemes of relative dimension at most one. The relative dimension zero case was conjectured by Qingyuan Jiang, and it gives a generalization of several known SOD such as Kapranov exceptional collections on Grassmannians. In relative dimension one case, it gives a new SOD of derived categories of punctual Quot schemes on smooth curves. The above SOD is applied to give interesting SOD of classical moduli spaces such as Brill-Noether loci, Hilbert schemes of points, etc. The idea is based on categorification problem of wall-crossing of Donaldson-Thomas theory for Calabi-Yau 3-folds, and the techniques involve window theorem, Koszul duality and categorical Hall products.