Speaker
Yukinobu Toda
(Tokyo)
Description
The McKay correspondence for Hilb^n(C^2) is its derived equivalence with C^{2n}/S_n, proven by Bridgeland-King-Reid and Haiman. In this talk, I will explan how to give its version for Hilb^n(C^3) using categorical DT theory and its categorical wall-crossing formula. It involves semiorthogonal decomposition with factors categorical Hall products of quasi-BPS categories, which we conjecture to be equivalent to the category of matrix factorizations over C^{3n}/S_n with zero potential. I explain that how (a variant of ) the above conjecture is implied by Betti geometric Langlands conjecture. This is a part of my series of joint works with Tudor Padurariu.
