In this talk,I will describe an analogue of Gromov-Witten theory associated to polynomial singularities.It was first introduced by Fan,Jarvis,and Ruan,and then an algebraic version has been developed by Polishchuk and Vaintrob using matrix factorizations.I will explain where the difficulty of actual computations in this theory comes from,and after rephrasing Polishchuk-Vaintrob construction in the language of K-theory,I will give my main result on the virtual fundamental cycle of the theory.I will give some of the ideas of the proof,based on some classical results about Koszul cohomology.