Related papers: Towards Generalizing Schubert Calculus in the Symp…

A previous result of the authors with Chaput and Perrin states that the union of all rational curves of fixed degree passing through a Schubert variety in a homogeneous space G/P is again a Schubert variety. In this paper we identify this…

The canonical analysis and subsequent quantization of the (2+1)-dimensional action of pure gravity plus a cosmological constant term is considered, under the assumption of the existence of one spacelike Killing vector field. The proper…

We study the Schubert calculus of the affine Grassmannian Gr of the symplectic group. The integral homology and cohomology rings of Gr are identified with dual Hopf algebras of symmetric functions, defined in terms of Schur's P and…

Let G be a compact connected Lie group, and (M,\omega) a Hamiltonian G-space with proper moment map \mu. We give a surjectivity result which expresses the K-theory of the symplectic quotient M//G in terms of the equivariant K-theory of the…

Given an action of a Compact Quantum Group (CQG) on a finite dimensional Hilbert space, we can construct an action on the associated Cuntz algebra. We study the fixed point algebra of this action, using Kirchberg classification results.…

In this note we prove the following theorem: Let $G$ be a compact Lie group acting on a compact symplectic manifold $M$ in a Hamiltonian fashion. If $L$ is an $l$-dimensional closed invariant submanifold of $M$, on which the $G$-action is…

We prove an explicit inverse Chevalley formula in the equivariant $K$-theory of semi-infinite flag manifolds of simply-laced type. By an inverse Chevalley formula, we mean a formula for the product of an equivariant scalar with a Schubert…

The main result of this paper is the description of asymptotics along rays in weight space of traces of equivariant Toeplitz operators composed with quantomorphisms for torus actions. The main ingredient in the proof is the microlocal…

The equivariant motivic Chern class of a Schubert cell in a `complete' flag manifold $X=G/B$ is an element in the equivariant K theory ring of $X$ to which one adjoins a formal parameter $y$. In this paper we prove several `folklore…

We present new definitions for and give a comprehensive treatment of the canonical compactification of configuration spaces due to Fulton-MacPherson and Axelrod-Singer in the setting of smooth manifolds, as well as a simplicial variant of…

We exhibit a finitely generated group $\M$ whose rational homology is isomorphic to the rational stable homology of the mapping class group. It is defined as a mapping class group associated to a surface $\su$ of infinite genus, and…

Let $M$ be a compact, connected symplectic manifold with a Hamiltonian action of a compact $n$-dimensional torus $G=T^n$. Suppose that $\sigma$ is an anti-symplectic involution compatible with the $G$-action. The real locus of $M$ is $X$,…

Hessenberg varieties are subvarieties of the flag variety parametrized by a linear operator $X$ and a nondecreasing function $h$. The family of Hessenberg varieties for regular $X$ is particularly important: they are used in quantum…

This paper is devoted to semi-classical aspects of symplectic reduction. Consider a compact prequantizable Kahler manifold M with a Hamiltonian torus action. Guillemin and Sternberg introduced an isomorphism between the invariant part of…

Homotopy comomentum maps are a higher generalization of the notion of moment map introduced to extend the concept of Hamiltonian actions to the framework of multisymplectic geometry. Loosely speaking, higher means passing from considering…

Let G be a complex semi-simple Lie group and let P,Q be a pair of parabolic subgroups of G such that Q contains P. Consider the flag varieties G/P, G/Q and Q/P. We show that certain structure constants in H^*(G/P) with respect to the…

In this article, we provide an exposition about symplectic toric manifolds, which are symplectic manifolds $(M^{2n}, \omega)$ equipped with an effective Hamiltonian $\mathbb{T}^n\cong (S^1)^n$-action. We summarize the construction of $M$ as…

Given a symplectic manifold, we ask in how many different ways can a torus act on it. Classification theorems in equivariant symplectic geometry can sometimes tell that two Hamiltonian torus actions are inequivalent, but often they do not…

We show the problem of counting homomorphisms from the fundamental group of a homology $3$-sphere $M$ to a finite, non-abelian simple group $G$ is #P-complete, in the case that $G$ is fixed and $M$ is the computational input. Similarly,…

We generalize the concept of global moment maps to local moment maps, whose different branches are labelled by the elements of the fundamental group of the underlying symplectic manifold. These branches can be smoothly glued together by…