A topological Chern character for matrix factorizations
김선우
27동 220호
0
56
10.06 14:43
| 구분 | 초청강연 |
|---|---|
| 일정 | 2026-11-09(월) 11:30~12:30 |
| 세미나실 | 27동 220호 |
| 강연자 | Mark Shoemaker (Colorado State University) |
| 담당교수 | 오정석 |
| 기타 |
Abstract: Let X be a smooth projective complex variety. The Chern character gives a homomorphism from K^0(X), the Grothendieck group of algebraic vector bundles on X, to H^*(X), the singular cohomology of X. The Grothendieck—Riemann—Roch theorem famously relates, for a map f: X —> X’, the induced pushforwards in K-theory and cohomology. The goal of this talk is to generalize this story to the setting of Landau—Ginzburg models, which consist, roughly, of a space together with a function.
Let Y be a smooth quasi-projective complex variety and w: Y —> \CC a regular function. Associated to the pair (Y, w) is the category MF(Y, w) of matrix factorizations of w, whose objects are “twisted" complexes of vector bundles, where the square of the differential is equal to multiplication by w. Let Y_- = Re(w)^{-1}(-\infy, 0) denote the set of points in Y such that the real part of w(y) is negative. I will construct a Chern character from the Grothendieck group of MF(Y, w) to the relative cohomology H*(Y, Y_-), and explain how a Grothendieck—Riemann—Roch type theorem can be deduced. If time permits I will describe an application to enumerative geometry.
