相关论文: Duistermaat-Heckman formula for a torus action on …

The main result of this paper is to study the local deformations of Calabi-Yau $\partial\bar{\partial}$-manifold that are co-polarised by the Gauduchon metric by considering the subfamily of co-polarised fibres by the class of Aeppli/De…

The most impressively prolific exploration of superstring models (aiming for our physical reality) has been focused on worldsheet-supersymmetric gauged linear sigma models and the closely associated complex-algebraic toric geometry. Mirror…

We introduce the notion of (Ramsey) action of a tree on a (filtered) semigroup. We then prove in this setting a general result providing a common generalization of the infinitary Gowers Ramsey theorem for multiple tetris operations, the…

If $K$ is a compact, connected, simply connected Lie group, its based loop group $\Omega K$ is endowed with a Hamiltonian $S^1 \times T$ action, where $T$ is a maximal torus of $K$. Atiyah and Pressley examined the image of $\Omega K$ under…

An action of a topological semigroup S on X is compactifiable if this action is a restriction of a jointly continuous action of S on a Hausdorff compact space Y. A topological semigroup S is compactifiable if the left action of S on itself…

Consider a Hamiltonian action of a compact connected Lie group on a conformal symplectic manifold. We prove a convexity theorem for the moment map under the assumption that the action is of Lee type, which establishes an analog of Kirwan's…

The Hamiltonian of the quantum Calogero-Sutherland model of $N$ identical particles on the circle with $1/r^{2}$ interactions has eigenfunctions consisting of Jack polynomials times the base state. By use of the generalized Jack polynomials…

Gaussian processes can be treated as subsets of a standard Hilbert space, however, the volume size relation between the underlying index space of random processes and its convex hull is not clear. The understanding of such volume size…

We define boundedness properties on the contractible fixed points set of the time-one map of an identity isotopy on a closed oriented surface with genus $g\geq1$. In symplectic geometry, a classical object is the notion of action function,…

We derive extensions of the monomialization theorems for morphisms of varieties in our earlier work. In this note we show that a local monomialization can be found which satisfies stronger local conditions. Some comments are made about how…

For a Kahler manifold (X, \omega) with a holomorphic line bundle L and metric h such that the Chern form of L is \omega, the spectral measures are the measures \mu_N = \sum |s_{N,i}|^2 \nu, where \{s_{N,i}\}_i is an L^2-orthonormal basis…

We prove a $C^\infty$ closing lemma for Hamiltonian diffeomorphisms of closed surfaces. This is a consequence of a $C^\infty$ closing lemma for Reeb flows on closed contact three-manifolds, which was recently proved as an application of…

We generalize Thomas-Yau's uniqueness theorem in two ways. We prove a stronger statement for special Lagrangians and include minimal Lagrangians in K\"ahler-Einstein manifold or more generally J-minimal Lagrangians introduced by Lotay and…

Compactifications of heterotic string theory on Generalized Calabi-Yau manifolds have been expected to give the same type of flexibility that type IIB compactifications on Calabi-Yau orientifolds have. In this note we generalize the work…

Consider the transverse isometric action of a finite dimensional Lie algebra g on a Riemannian foliation. This paper studies the equivariant Morse-Bott theory on the leaf space of the Riemannian foliations in this setting. Among other…

An important combinatorial result in equivariant cohomology and $K$-theory Schubert calculus is represented by the formulas of Billey and Graham-Willems for the localization of Schubert classes at torus fixed points. These formulas work…

Let $G$ be a complex Lie group acting on a compact complex Hermitian manifold $M$ by holomorphic isometries. We prove that the induced action on the Dolbeault cohomology and on the Bott-Chern cohomology is trivial. We also apply this result…

In this paper we study the size of the fixed point set of a Hamiltonian diffeomorphism on a closed symplectic manifold which is both rational and weakly monotone. We show that there exists a non-trivial cycle of fixed points whenever the…

The celebrated Fefferman's theorems on the general form of linear functionals on the Hardy space $H^1$ over the circle group is generalized to the case of an arbitrary compact Abelian group with totally ordered dual. Several corollaries…

We give a presentation of the cohomology ring of spatial polygon spaces $M(r)$ with fixed side lengths $r \in \mathbb R^n_+$. These spaces can be described as the symplectic reduction of the Grassmaniann of 2-planes in $\mathbb C^n$ by the…