Related papers: Explicit correspondences between gradient trees in…

For given smooth functions $(f_1,\dots,f_n)$ on $M$, Fukaya and Oh showed that the moduli space of pseudoholomorphic disks in $T^*M$ which are bounded by Lagrangian sections $\{L_i^\epsilon=\operatorname{graph}(\epsilon df_i)\}$ is…

Let $G$ be a connected compact Lie group and let $\mathbb{G}$ be its complexification. In this paper, we establish a correspondence between the moduli spaces of holomorphic disks bounded by a $G$-invariant Lagrangian submanifold $L…

We describe a family of calibrations arising naturally on a hyperk\"ahler manifold $M$. These calibrations calibrate the holomorphic Lagrangian, holomorphic isotropic and holomorphic coisotropic subvarieties. When $M$ is an HKT…

We simplify proof of the theorem that close to any pseudoholomorphic disk there passes a pseudoholomorphic disk of arbitrary close size with any pre-described sufficiently close direction. We apply these results to the Kobayashi and Hanh…

In the recursive lamination of the disk, one tries to add chords one after another at random; a chord is kept and inserted if it does not intersect any of the previously inserted ones. Curien and Le Gall [Ann. Probab. 39 (2011) 2224-2270]…

Let $L$ be a compact oriented Lagrangian surface in a K\"ahler surface endowed with a complete Riemannian metric (compatible with the symplectic structure and the complex structure) with bounded sectional curvatures and a positive lower…

We introduce the tree distance, a new distance measure on graphs. The tree distance can be computed in polynomial time with standard methods from convex optimization. It is based on the notion of fractional isomorphism, a characterization…

On a compact connected Riemann surface $C$ of genus at least $2$, we construct Lagrangian correspondences between moduli spaces of rank-$n$ Higgs bundles (respectively, holomorphic connections) and the Hilbert schemes of points on $T^\ast…

We consider the Steiner tree problem in hyperbolic geometry in the context of the AdS/CFT duality between large-$c$ conformal blocks on the boundary and particle motions in the bulk. The Steiner trees are weighted graphs on the Poincare…

We consider the dimer model on piecewise Temperleyan, simply connected domains, on families of graphs which include the square lattice as well as superposition graphs. We focus on the spanning tree $\mathcal{T}_\delta$ associated to this…

First, we provide another proof that the signed count of the real $J$-holomorphic spheres (or $J$-holomorphic discs) passing through a generic real configuration of $k$ points is independent of the choice of the real configuration and the…

Kashiwara, Polesello, Schapira and D'Agnolo defined canonical deformation quantizations of a holomorphic symplectic manifold and a holomorphic Lagrangian submanifold equipped with an orientation data. The goal of this paper is to use…

We present a new method for classifying naturally reductive homogeneous spaces -- i.\,e.~homogeneous Riemannian manifolds admitting a metric connection with skew torsion that has parallel torsion \emph{and} curvature. This method is based…

Let $D(M,N)$ be the set of integers that can be realized as the degree of a map between two closed connected orientable manifolds $M$ and $N$ of the same dimension. For closed $3$-manifolds with $S^3$-geometry $M$ and $N$, every such degree…

For a harmonic diffeomorphism between the Poincar\'{e} disks, Wan showed the equivalence between the boundedness of the Hopf differential and the quasi-conformality. In this paper, we will generalize this result from quadratic differentials…

We derive explicit isomorphisms between certain congruence subgroups of the Siegel modular group, the Hermitian modular group over an arbitrary imaginary-quadratic number field and the modular group over the Hurwitz quaternions of degree 2…

In his 1989 paper, Floer established a connection between holomorphic strips with boundary on a Lagrangian $L$ and a small Hamiltonian push-off $L_{f}$, and gradient flow lines for the function $f$. The present paper studies the compactness…

In the objective of studying concentration and oscillation properties of eigenfunctions of the discrete Laplacian on regular graphs, we construct a pseudo-differential calculus on homogeneous trees, their universal covers. We define symbol…

Given a convex $n$-gon, we can draw $n$ disks (called side disks) where each disk has a different side of the polygon as diameter and the midpoint of the side as its center. The intersection graph of such disks is the undirected graph with…

In this paper, we study uniform rooted plane trees with given degree sequence. We show, under some natural hypotheses on the degree sequence, that these trees converge toward the so-called Inhomogeneous Continuum Random Tree after…