Abstract:
In recent years, graded matrix factorization categories have played important roles in the LG-LG version of homological mirror symmetry conjecture which was proposed by M.Kontsevich. Let $W$ be a quasi-homogeneous polynomial with an isolated singularity at origin. In this talk, I will first talk about some results of noncommutative projective scheme in the sense of Artin-Zhang defined by $W$, including Serre-duality, vanishing theorem and so on. Building on this basis, I will discuss the relation between the existence of tilting objects and Hochschild homology groups of the graded matrix factorization category defined by $W$. Finally, I will introduce some applications in the state spaces of FJRW theory and tilting Cohen-Macaulay representations.
