In this paper we consider three types of localization theorems for algebraic stacks:(i)
Concentration, or cohomological localization. Given an algebraic group acting on a scheme …

We prove the abelian–nonabelian correspondence for quasimap-functions. That is, if is an
affine lci variety with an action by a complex reductive group, we prove an explicit formula …

We introduce the notion of log R-maps, and develop a proper moduli stack of stable log R-
maps in the case of a hybrid gauged linear sigma model. Two virtual cycles (canonical and …

We study algebraicity and smoothness of fixed point stacks for flat group schemes which
have a finite composition series whose factors are either reductive or proper, flat, finitely …

Given one quasi-smooth derived space cut out of another by a section of a 2-term complex
of bundles, we give two formulae for its virtual cycle. They are modelled on the the-fields …

Given a triple (X, E, s) of a smooth projective variety, a rank r vector bundle and a regular
section, we construct a moduli of stable maps to X with fields together with a cosection …

For a two-periodic complex of vector bundles, Polishchuk and Vaintrob have constructed its
localized Chern character. We explore some basic properties of this localized Chern …

The theory of Mixed-Spin-P (MSP) fields was introduced by Chang-Li-Li-Liu for the quintic
threefold, aiming at studying its higher-genus Gromov-Witten invariants. Chang-Guo-Li has …

By the reduced component in a moduli space of stable quasimaps to n-dimensional
projective space P n we mean the closure of the locus in which the domain curves are …

We introduce a technique for proving all-genus wall-crossing formulas in the gauged linear
sigma model as the stability parameter varies, without assuming factorization properties of …