For a generic quasi-symmetric representation X of a reductive group G, the GIT quotient stack [X(L)//G] for a generic polarization L is a (stacky) crepant resolution of the affine quotient X/G. Halpern-Leistner and Sam proved that the GIT quotients [X(L)//G] are all derived equivalent, which proved Bondal-Orlov conjecture for [X(L)//G]. One of the key ingredient of Halpern-Leistner--Sam’s work is a magic window, which is shown to be equivalent to the derived category of the GIT quotient [X(L)//G]. A magic window is also equivalent to the derived category of a noncommutative crepant resolution (NCCR) of X/G, which is the endomorphism algebra End(M) of a certain module M over X/G. In this talk, we explain that the modules giving NCCR of X/G are related by certain operations called exchanges, and in the case when G is a torus, the modules are related by Iyama--Wemyss mutations. If time permits, I will explain that certain autoequivalences of a Calabi-Yau hypersurface correspond to the compositions of Iyama--Wemyss mutations via matrix factorizations.

This seminar is a hybrid meeting.
Zoom Meeting ID: 823 1020 3999
Passcode: 794766