相关论文: Contact isotopies in the coherent-constructible co…

Let $\Sigma$ be a fan inside the lattice $\mathbb{Z}^n$, and $\mathcal{E}:\mathbb{Z}^n \rightarrow \operatorname{Pic}{S}$ be a map of abelian groups. We introduce the notion of a principal toric fibration $\mathcal{X}_{\Sigma, \mathcal{E}}$…

A morphism from a diagonalizable group $G$ to the torus of a toric variety $X$ induces an action of $G$ on $X$. We prove the category of ind-coherent sheaves on the quotient stack is equivalent to the category of sheaves on a cover of a…

The nonequivariant coherent-costructible correspondence is a microlocal-geometric interpretation of homological mirror symmetry for toric varieties conjectured by Fang-Liu-Treumann-Zaslow. We prove a generalization of this conjecture for a…

The coherent-constructible correspondence is a relationship between coherent sheaves on a toric variety X, and constructible sheaves on a real torus T. This was discovered by Bondal, and explored in the equivariant setting by Fang, Liu,…

Let $X_\Sigma$ be a complete toric variety. The coherent-constructible correspondence $\kappa$ of \cite{FLTZ} equates $\Perf_T(X_\Sigma)$ with a subcategory $Sh_{cc}(M_\bR;\LS)$ of constructible sheaves on a vector space $M_\bR.$ The…

We prove that a topological contact isotopy uniquely defines a topological contact Hamiltonian. Combined with previous results from [MS11], this generalizes the classical one-to-one correspondence between smooth contact isotopies and their…

The sheaf-function correspondence identifies the group of constructible functions on a real analytic manifold $M$ with the Grothendieck group of constructible sheaves on $M$. When $M$ is a finite dimensional real vector space,…

We prove that for regular contact forms there exists a bijective correspondence between the $C^0$ limits of sequences of smooth strictly contact isotopies and the limits with respect to the contact distance of their corresponding…

We continue the mathematical development of the open/closed correspondence proposed by Mayr and Lerche-Mayr. Given an open geometry on a toric Calabi-Yau 3-orbifold $\mathcal{X}$ relative to a framed Aganagic-Vafa outer brane…

The classical Riemann-Hilbert correspondence establishes an equivalence between the triangulated category of regular holonomic D-modules and that of constructible sheaves. In this paper, we prove a Riemann-Hilbert correspondence for…

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 Lagrangian (real, complex) projective spaces $K_1, \dots , K_m$ in a Liouville manifold $(X, \omega)$ satisfying a certain cohomological condition, we show there is a Lagrangian correspondence that assigns a Lagrangian sphere $L_i…

Given a consistent bipartite graph $\Gamma$ in $T^2$ with a complex-valued edge weighting $\mathcal{E}$ we show the following two constructions are the same. The first is to form the Kasteleyn operator of $(\Gamma, \mathcal{E})$ and pass to…

We study the open/closed correspondence for the projective line via mirror symmetry. More explicitly, we establish a correspondence between the generating function of disk Gromov-Witten invariants of the complex projective line…

Let $(G,\alpha)$ and $(H,\beta)$ be locally compact Hausdorff groupoids with Haar systems, and let $(X,\lambda)$ be a topological correspondence from $(G,\alpha)$ to $(H,\beta)$ which induce the ${C}^*$-correspondence $\mathcal{H}(X)\colon…

We show that every open book decomposition of a contact 3-manifold can be represented (up to isotopy) by a smooth R-invariant family of pseudoholomorphic curves on its symplectization with respect to a suitable stable Hamiltonian structure.…

A hyperkaehler manifold with a circle action fixing just one complex structure admits a natural a hyperholomorphic line bundle. This forms the basis for the construction of a corresponding quaternionic Kaehler manifold in the work of…

This is an expository article describing recent results of the authors and David Nadler on microlocalization, the Fukaya category, and coherent sheaves on toric varieties. The original papers are arXiv:math/0604379, arXiv:math/0612399 and…

The derived category of coherent sheaves $\mathcal{T}_B$ associated to a birational cobordism which is either a weighted projective space, a stacky Atiyah flip, or a stacky blow-up of a point has a conjectural mirror Fukaya-Seidel category…

We analytically derive a compatible family of effective field theories that uniquely describe topological superconductors in 3D, their 2D boundary and their 1D defect lines. We start by deriving the topological field theory of a 3D…