Pinharry, Michelle2020-09-222020-09-222020-07https://hdl.handle.net/11299/216347University of Minnesota Ph.D. dissertation. July 2020. Major: Mathematics. Advisor: Ionut Ciocan-Fontanine. 1 computer file (PDF); iv, 50 pages.The aim of this paper is to prove a wall-crossing formula at the level of virtual fundamental classes of weighted stable quasimaps to a class of GIT quotients via localization. The idea of the proof is to use virtual localization on a larger moduli space, referred to as the ``master space'', the fixed-point loci of which are in one-to-one correspondence with the terms in the wall-crossing formula. As an immediate application, we obtain the modified string and dilaton equations for stable quasimaps to GIT quotients.enAlgebraic GeometryQuasimapsWallcrossingThesis or Dissertation