  These expository notes are based on a series of lectures given at the May
2018 Snowbird workshop, Crossing the Walls in Enumerative Geometry. We give an
introductory treatment of the notion of a virtual fundamental class in
algebraic geometry, and describe a new construction of the virtual fundamental
class for Gromov-Witten theory of a hypersurface. The results presented here
are based on joint work with I. Ciocan-Fontanine, D. Favero, J. Gu\'er\'e, and
B. Kim.
