Related papers: Generating Functions in $\mathbb{R}^{2n}$ and the …

Persistence modules and barcodes are used in symplectic topology to define various invariants of Hamiltonian diffeomorphisms, however numerical methods for computing these barcodes are not yet well developed. In this paper we define one…

We use algebraic methods to compute the simple Hurwitz numbers for arbitrary source and target Riemann surfaces. For an elliptic curve target, we reproduce the results previously obtained by string theorists. Motivated by the Gromov-Witten…

We construct a generating functional for the exact evalutation of a coherent representation of spin network amplitudes. This generating functional is defined for arbitrary graphs and depends only on a pair of spinors for each edge. The…

Analytical expressions of some of the spin-spin correlation functions up to eight lattice sites for the spin-1/2 anti-ferromagnetic Heisenberg chain at zero temperature without magnetic field are obtained. The key object of our method is…

We derive several new applications of the concept of sequences of Laplacian cut-off functions on Riemannian manifolds (which we prove to exist on geodesically complete Riemannian manifolds with nonnegative Ricci curvature): In particular,…

We study the generating function of rooted and unrooted hyperforests in a general complete hypergraph with n vertices by using a novel Grassmann representation of their generating functions. We show that this new approach encodes the known…

We consider a space of infinitely smooth functions on an unbounded closed convex set in ${\mathbb R}^n$. It is shown that each function of this space can be extended to an entire function in ${\mathbb C}^n$ satisfying some prescribed growth…

MacMahon's classic generating function of random plane partitions, which is related to Schur polynomials, was recently extended by Vuletic to a generating function of weighted plane partitions that is related to Hall-Littlewood polynomials,…

We prove that the Grassmannian of totally isotropic $k$-spaces of the polar space associated to the unitary group $\mathsf{SU}_{2n}(\mathbb{F})$ ($n\in \mathbb{N}$) has generating rank ${2n\choose k}$ when $\mathbb{F}\ne \mathbb{F}_4$. We…

Let $X_n(K)$ be a building of Coxeter type $X_n = A_n$ or $X_n = D_n$ defined over a given division ring $K$ (a field when $X_n = D_n$). For a non-connected set $J$ of nodes of the diagram $X_n$, let $\Gamma(K) = Gr_J(X_n(K))$ be the…

Lipschitz and horizontal maps from an $n$-dimensional space into the $(2n+1)$-dimensional Heisenberg group $\H^n$ are abundant, while maps from higher-dimensional spaces are much more restricted. DeJarnette-Haj{\l}asz-Lukyanenko-Tyson…

In this paper we analyse the structure of the spaces of smooth type functions, generated by elements of arbitrary Hilbert spaces, as a continuation of the research in our previous papers in this series. We prove that these spaces are…

Recently, a universal formula for a non-holomorphic modular completion of the generating functions of refined BPS indices in various theories with $N=2$ supersymmetry has been suggested. It expresses the completion through the holomorphic…

We use exact Lagrangian fillings and Weinstein handlebody diagrams to construct infinitely many distinct exact Lagrangian tori in $4$-dimensional Milnor fibers of isolated hypersurface singularities with positive modality. We also provide a…

We examine the $L^2$-topology of the gauge orbits over a closed Riemann surface. We prove a subtle local slice theorem based on the div-curl Lemma of harmonic analysis, and deduce local pathwise connectedness and local uniform…

Let us consider a truncated matroid $M_{\Gamma}^{r}$ of rank $r$ of a graphic matroid of a graph $\Gamma$. The basis for $M_{\Gamma}^{r}$ is the set of the forests with $r$ edges in $\Gamma$. We consider this basis generating function and…

In this article, we modify the proof of holomorphic quilts from Wehrheim and Woodward in \cite{wehrheim2009floer} to construct a specific type of immersed holomorphic quilt, where the symplectic manifolds are closed surfaces. The…

We study a generating function for the sum over fatgraphs with specified valences of vertices and faces, inversely weighted by the order of their symmetry group. A compact expression is found for general (i.e. non necessarily connected)…

We construct, for a homogeneous Lagrangian of arbitrary order in two independent variables, a differential 2-form with the property that it is closed precisely when the Lagrangian is null. This is similar to the property of the `fundamental…

We decompose the generating function $\sum_{n=0}^\infty\binom{2n}nP_n(y)^2z^n$ of the squares of Legendre polynomials as a product of periods of hyperelliptic curves. These periods satisfy a family of $\textit{second}$ order differential…