Bumsig Kim: Virtual Factorizations

Abstract: In this talk, based on joint work with David Favero, we explain how to define an A-side cohomological field theory for a given gauged linear sigma model (GLSM). For this, we follow the approach by Polishchuk -- Vaintrob, i.e., we construct a virtual factorization on a suitable smooth stack U containing the moduli space LGQ of Landau-Ginzburg stable (quasi)maps. The latter moduli space LGQ was introduced by Fan, Jarvis and Ruan. The state space taken is the hypercohomology of Hodge complex twisted by the superpotential of GLSM in the inertia stack of the associated DM stack of GLSM. We will use the notion of Atiyah class of global matrix factorizations from a joint work with A. Polishchuk and a simplified construction of the ambient stack U from a previous joint work with I. Ciocan-Fontanine, D. Favero, J. Guere, M. Shoemaker.