Related papers: Equivariant Jeffrey-Kirwan localization theorem in…

In this paper we review the quantization procedure employed by Jeffrey and Weitsman in their formalization of Witten's three manifold invariants. In so doing, we formalize the stratification of the Lagrangian leaf which corresponds to the…

We construct Witten instanton complexes for K\"ahler Hamiltonian Morse functions on stratified pseudomanifolds with wedge K\"ahler metrics satisfying a local conformally totally geodesic condition. We use this to extend Witten's holomorphic…

We survey recent contributions to finite element exterior calculus on manifolds and surfaces within a comprehensive formalism for the error analysis of vector-valued partial differential equations on manifolds. Our primary focus is on…

Let T be a compact torus and X a nice compact T-space (say a manifold or variety). We introduce a functor assigning to X a "GKM-sheaf" F_X over a "GKM-hypergraph" G_X. Under the condition that X is equivariantly formal, the ring of global…

We describe vector valued conjugacy equivariant functions on a group K in two cases -- K is a compact simple Lie group, and K is an affine Lie group. We construct such functions as weighted traces of certain intertwining operators between…

Let $S$ be the affine plane $\C^2$ together with an appropriate $\mathbb T = \C^*$ action. Let $\hil{m,m+1}$ be the incidence Hilbert scheme. Parallel to \cite{LQ}, we construct an infinite dimensional Lie algebra that acts on the direct…

We study the hyperk\"ahler analogues of moduli spaces of semistable n-gons in complex projective space. We prove that the hyperk\"ahler Kirwan map is surjective and produce a formula that recursively calculates the Betti numbers of these…

In this paper we first consider the Hamiltonian action of a compact connected Lie group on an $H$-twisted generalized complex manifold $M$. Given such an action, we define generalized equivariant cohomology and generalized equivariant…

The locality conditions for the vanishing of local anomalies in field theory are shown to admit a geometrical interpretation in terms of local equivariant cohomology, thus providing a method to deal with the problem of locality in the…

We study the Witten--Reshetikhin--Turaev SU(2) invariant for the Seifert manifold with 4-singular fibers. We define the Eichler integrals of the modular forms with half-integral weight, and we show that the invariant is rewritten as a sum…

We develop some useful techinques for integrating over Higgs branches in supersymmetric theories with 4 and 8 supercharges. In particular, we define a regularized volume for hyperkahler quotients. We evaluate this volume for certain ALE and…

The aim of this short paper is two-fold: (i) to construct a TQ-localization functor on algebras over a spectral operad O, in the case where no connectivity assumptions are made on the O-algebras, and (ii) more generally, to establish the…

It is shown that Parisi-Sourlas supersymmetry of stochastic quantization is a Cartan model of equivariant cohomology. Equivariant cohomological structure of stochastic quantization of linear and non-linear sigma models are discussed.…

In this paper we identify the problem of equivariant vortex counting in a $(2,2)$ supersymmetric two dimensional quiver gauged linear sigma model with that of computing the equivariant Gromov-Witten invariants of the GIT quotient target…

As a generalization of our previous paper [GK], we formulate a residue formula and some simple behaviors of equivariant quantum cohomology applying to compute the quantum cohomology of partial flag manifolds $F_{k_1,\cdots , k_l} $with a…

This work deals with relations between a bounded cohomological invariant and the geometry of Hermitian symmetric spaces of noncompact type. The invariant, obtained from the K\"ahler class, is used to define and characterize a special class…

Let $G$ be a compact Lie group. We study a class of Hamiltonian $(G \times S^{1})$-manifolds decorated with a function $s$ with certain equivariance properties, under conditions on the $G$-action which we call of (semi-)linear type. In this…

We study the almost Kaehler geometry of adjoint orbits of non-compact real semisimple Lie groups endowed with the Kirillov-Kostant-Souriau symplectic form and a canonically defined almost complex structure. We give explicit formulas for the…

We extend the construction of generalized Berezin and Berezin-Toeplitz quantization to the case of compact Hodge supermanifolds. Our approach is based on certain super-analogues of Rawnsley's coherent states. As applications, we discuss the…

In [Azimzadeh, P., and P. A. Forsyth. "Weakly chained matrices, policy iteration, and impulse control." SIAM J. Num. Anal. 54.3 (2016): 1341-1364], we outlined the theory and implementation of computational methods for implicit schemes for…