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Weyl symbols and boundedness of Toeplitz operatorsJul 13 2019We study Toeplitz operators on the Bargmann space, with Toeplitz symbols that are exponentials of inhomogeneous quadratic polynomials. It is shown that the boundedness of such operators is implied by the boundedness of the corresponding Weyl symbols.

The royal road to automatic noncommutative real analyticity, monotonicity, and convexityJul 12 2019It was shown classically that matrix monotone and matrix convex functions must be real analytic by L\"owner and Kraus respectively. Recently, various analogues have been found in several noncommuting variables. We develop a general framework for lifting ... More

Dilation theory and analytic model theory for doubly commuting sequences of $C_{.0}$-contractionsJul 12 2019Sz.-Nagy and Foias proved that each $C_{\cdot0}$-contraction has a dilation to a Hardy shift and thus established an elegant analytic functional model for contractions of class $C_{\cdot0}$. This has motivated lots of further works on model theory and ... More

A Regionalisation Approach for Rainfall based on Extremal DependenceJul 12 2019To mitigate the risk posed by extreme rainfall events, we require statistical models that reliably capture extremes in continuous space with dependence. However, assuming a stationary dependence structure in such models is often erroneous, particularly ... More

Global bifurcation of waves with multiple critical layersJul 12 2019Analytic global bifurcation theory is used to construct a large variety of families of steady periodic two-dimensional gravity water waves with real-analytic vorticity distributions, propagating in an incompressible fluid. The waves that are constructed ... More

Gittins' theorem under uncertaintyJul 12 2019We study dynamic allocation problems for discrete time multi-armed bandits under uncertainty, based on the the theory of nonlinear expectations. We show that, under strong independence of the bandits and with some relaxation in the definition of optimality, ... More

Commutant lifting and Nevanlinna-Pick interpolation in several variablesJul 11 2019This paper concerns a commutant lifting theorem and a Nevanlinna-Pick type interpolation result in the setting of multipliers from vector-valued Drury-Arveson space to a large class of vector-valued reproducing kernel Hilbert spaces over the unit ball ... More

Optimal destabilization of K-unstable Fano varieties via stability thresholdsJul 11 2019We show that for a K-unstable Fano variety, any divisorial valuation computing its stability threshold induces a non-trivial special test configuration preserving the stability threshold. When such a divisorial valuation exists, we show that the Fano ... More

Bernstein--Sato Varieties, $\mathscr{D}_{X}[S]F^{S}$, the Map $\nabla_{A}$, and Cohomology Support LociJul 11 2019Given a complex germ $f$ near the point $\mathfrak{x}$ of the complex manifold $X$, equipped with a factorization $f = f_{1} \cdots f_{r}$, we consider the $\mathscr{D}_{X,\mathfrak{x}}[s_{1}, \dots, s_{r}]$-module generated by $ F^{S} := f_{1}^{s_{1}} ... More

Invariants of formal pseudodifferential operator algebras and algebraic modular formsJul 11 2019We study from an algebraic point of view the question of extending an action of a group \(\Gamma\) on a commutative domain \(R\) to a formal pseudodifferential operator ring \(B=R(\!(x\,;\,d)\!)\) with coefficients in \(R\), as well as to some canonical ... More

Further remarks on rigidity of Hénon mapsJul 11 2019For a H\'{e}non map $H$ in $\mathbb{C}^2$, we characterize the polynomial automorphisms of $\mathbb{C}^2$ which keep any fixed level set of the Green function of $H$ completely invariant. The interior of any non-zero sublevel set of the Green function ... More

Fixed point branes, singular loci and mirror symmetryJul 10 2019This is the extended abstract of the talk given at the workshop "Geometry and physics of Higgs bundles", held at the Mathematisches Forschungsinstitut Oberwolfach in May 2019.

Tensor-Free Proximal Methods for Lifted Bilinear/Quadratic Inverse Problems with Applications to Phase RetrievalJul 10 2019We propose and study a class of novel algorithms that aim at solving bilinear and quadratic inverse problems. Using a convex relaxation based on tensorial lifting, and applying first-order proximal algorithms, these problems could be solved numerically ... More

Dreaming machine learning: Lipschitz extensions for reinforcement learning on financial marketsJul 09 2019We develop a new topological structure for the construction of a reinforcement learning model in the framework of financial markets. It is based on Lipschitz type extension of reward functions defined in metric spaces. Using some known states of a dynamical ... More

Arithmetic topology of 4-manifoldsJul 08 2019We construct a functor from the smooth 4-dimensional manifolds to the hyper-algebraic number fields, i.e. fields with a non-commutative multiplication. It is proved that that the simply connected 4-manifolds correspond to the abelian extensions. As a ... More

The Power of Comparisons for Actively Learning Linear ClassifiersJul 08 2019In the world of big data, large but costly to label datasets dominate many fields. Active learning, an unsupervised alternative to the standard PAC-learning model, was introduced to explore whether adaptive labeling could learn concepts with exponentially ... More

Period integrals from wall structures via tropical cycles, canonical coordinates in mirror symmetry and analyticity of toric degenerationsJul 08 2019We give a simple expression for the integral of the canonical holomorphic volume form in degenerating families of varieties constructed from wall structures and with central fiber a union of toric varieties. The cycles to integrate over are constructed ... More

Commutative Lie algebras and commutative cohomology in characteristic $2$Jul 08 2019We discuss a version of the Chevalley--Eilenberg cohomology in characteristic $2$, where the alternating cochains are replaced by symmetric ones.

On Competing Definitions for the Diederich-Fornæss IndexJul 08 2019Let $\Omega\subset\mathbb{C}^n$ be a bounded pseudoconvex domain. We define the Diederich-Forn{\ae}ss index with respect to a family of functions to be the supremum over the set of all exponents $0<\eta<1$ such that there exists a function $\rho_\eta$ ... More

Higher order polars of quasi-ordinary singularitiesJul 07 2019A quasi-ordinary polynomial is a monic polynomial with coefficients in the power series ring such that its discriminant equals a monomial up to unit. In this paper we study higher derivatives of quasi-ordinary polynomials, also called higher order polars. ... More

Two-dimensional twistor manifolds and Teukolsky operatorsJul 04 2019The Teukolsky equations are currently the leading approach for analysing stability of linear massless fields propagating in rotating black holes. It has recently been shown that the geometry of these equations can be understood in terms of a connection ... More

On the continuous extension of Kobayashi isometriesJul 04 2019We provide a sufficient condition for the continuous extension of isometries for the Kobayashi distance between bounded convex domains in complex Euclidean spaces having boundaries that are only slightly more regular than $\mathcal{C}^1$. This is a generalization ... More

The Bruce-Roberts number of a function on a hypersurface with isolated singularityJul 04 2019Let $(X,0)$ be an isolated hypersurface singularity defined by $\phi\colon(\mathbb C^n,0)\to(\mathbb C,0)$ and $f\colon(\mathbb C^n,0)\to\mathbb C$ such that the Bruce-Roberts number $\mu_{BR}(f,X)$ is finite. We first prove that $\mu_{BR}(f,X)=\mu(f)+\mu(\phi,f)+\mu(X,0)-\tau(X,0)$, ... More

Continuity and Bargmann mapping properties of quasi-Banach Orlicz modulation spacesJul 04 2019We deduce continuity, compactness and invariance properties for quasi-Banach Orlicz modulation spaces. We characterize such spaces in terms of Gabor expansions and by their images under the Bargmann transform.

Isometric copies of $\ell_\infty^n$ and $\ell_1^n$ in transportation cost spaces on finite metric spacesJul 02 2019Main results: (a) If a metric space contains $2n$ elements, the transportation cost space on it contains a $1$-complemented isometric copy of $\ell_1^n$. (b) An example of a finite metric space whose transportation cost space contains an isometric copy ... More

Cryo-EM reconstruction of continuous heterogeneity by Laplacian spectral volumesJul 01 2019Single-particle electron cryomicroscopy is an essential tool for high-resolution 3D reconstruction of proteins and other biological macromolecules. An important challenge in cryo-EM is the reconstruction of non-rigid molecules with parts that move and ... More

On the generation of rank 3 simple matroids with an application to Terao's freeness conjectureJul 01 2019In this paper we describe a parallel algorithm for generating all non-isomorphic rank $3$ simple matroids with a given multiplicity vector. We apply our implementation in the HPC version of GAP to generate all rank $3$ simple matroids with at most $14$ ... More

Applications of Zalcman's lemma in $C^n$Jul 01 2019The aim of this paper is to give some applications of Zalcman's Rescalling Lemma.

On the degeneracy of integral points and entire curves in the complement of nef effective divisorsJul 01 2019As a consequence of our recently established generalized Schmidt's subspace theorem for closed subschemes in general position, we prove a degeneracy theorem for integral points on the complement of a union of nef effective divisors. A novel aspect of ... More

Complex structures and slice-regular functions on real associative algebrasJul 01 2019In this paper, we study the (complex) geometry of the set $S$ of the square roots of $-1$ in a real associative algebra $A$, showing that $S$ carries a natural complex structure, given by an embedding into the Grassmannian of $\mathbb{C}\otimes A$. With ... More

The CR Ahlfors derivative and a new invariant for spherically equivalent CR mapsJul 01 2019We study a CR analogue of the Ahlfors derivative for conformal immersions of Stowe [23] that generalizes the CR Schwarzian derivative studied earlier by the second-named author [21]. This notion possesses several important properties similar to those ... More

A transcendental dynamical degreeJul 01 2019We give an example of a dominant rational selfmap of the projective plane whose dynamical degree is a transcendental number.

Quantum harmonic analysis on lattices and Gabor multipliersJun 30 2019We develop a theory of quantum harmonic analysis on lattices in $\mathbb{R}^{2d}$. Convolutions of a sequence with an operator and of two operators are defined over a lattice, and using corresponding Fourier transforms of sequences and operators we develop ... More

Weighted Sobolev $L^{p}$ estimates for homotopy operators on strictly pseudoconvex domains with $C^{2}$ boundaryJun 29 2019We derive estimates in a weighted Sobolev space $W^{k,p}_{\mu}(D)$ for a homotopy operator on a bounded strictly pseudoconvex domain $D$ of $C^2$ boundary in ${\C}^n$. As a result, we show that given any $2n < p < \infty$, $k > 1$, $q \geq 1$, and a $\dbar$-closed ... More

Free abelian group actions on normal projective varieties: sub-maximal dynamical rank caseJun 29 2019Let $X$ be a normal projective variety of dimension $n$ and $G$ an abelian group of automorphisms such that all elements of $G\setminus \{\mathrm{id}\}$ are of positive entropy. Dinh and Sibony showed that $G$ is actually free abelian of rank $\le n - ... More

Some properties of $h$-extendible domains in $\mathbb C^{n+1}$Jun 29 2019Jul 06 2019The purpose of this article is twofold. The first aim is to characterize $h$-extendibility of smoothly bounded pseudoconvex domains in $\mathbb C^{n+1}$ by their noncompact automorphism groups. Our second goal is to show that if the squeezing function ... More

Some properties of $H$-extendible domains in $\mathbb C^{n+1}$Jun 29 2019The purpose of this article is twofold. The first aim is to characterize $h$-extendibility of smoothly bounded pseudoconvex domains in $\mathbb C^{n+1}$ by their noncompact automorphism groups. Our second goal is to show that if the squeezing function ... More

Quadrature by Two Expansions: Evaluating Laplace Layer Potentials using Complex Polynomial and Plane Wave ExpansionsJun 28 2019The recently developed quadrature by expansion (QBX) technique accurately evaluates the layer potentials with singular, weakly or nearly singular, or even hyper singular kernels in the integral equation reformulations of partial differential equations. ... More

Large-scale inference with block structureJun 28 2019The detection of weak and rare effects in large amounts of data arises in a number of modern data analysis problems. Known results show that in this situation the potential of statistical inference is severely limited by the large-scale multiple testing ... More

Engel structures on complex surfacesJun 28 2019We classify complex surfaces $(M,\,J)$ admitting Engel structures $\mathcal{D}$ which are complex line bundles. Namely we prove that this happens if and only if $(M,\,J)$ has trivial Chern classes. We construct examples of such Engel structures by adapting ... More

On spherical unitary representations of groups of spheromorphisms of Bruhat--Tits treesJun 28 2019Consider an infinite homogeneous tree $T_n$ of valence $n+1$, its group $Aut(T_n)$ of automorphisms, and the group $Hie(T_n)$ of its spheromorphisms (hierarchomorphisms), i.~e., the group of homeomorphisms of the boundary of $T_n$ that locally coincide ... More

Detection of time-varying heat sources using an analytic forward modelJun 28 2019We present a simple, analytic point source model for both static and time-varying point-like heat sources and the resulting temperature profile that solves the heat equation in dimension three. Simple algorithms to detect the location and spectral content ... More

The multidimensional truncated Moment Problem: Shape and Gaussian Mixture Reconstruction from Derivatives of MomentsJun 28 2019In this paper we introduce the theory of derivatives of moments and (moment) functionals to represent moment functionals by Gaussian mixtures, characteristic functions of polytopes, and simple functions of polytopes. We study, among other measures, Gaussian ... More

A global Torelli theorem for certain Calabi-Yau threefoldsJun 28 2019We establish a global Torelli theorem for the complete family of Calabi-Yau threefolds arising from cyclic triple covers of $\mathbb P^3$ branched along stable hyperplane arrangements.

Singular Points of High Multiplicity for Septic CurvesJun 26 2019For real irreducible algebraic curves of the seventh degree, there are 22 types of singular points of multiplicity six, 174 types of singular points of multiplicity five, and at least 182 types of singular points of multiplicity four. For complex irreducible ... More

A double mean field equation related to a curvature prescription problemJun 26 2019We study a double mean field--type PDE related to a prescribed curvature problem on compacts surfaces with boundary. We provide a general blow--up analysis, then a Moser--Trudinger inequality, which gives energy--minimizing solutions for some range of ... More

Spectral Properties of Radial Kernels and Clustering in High DimensionsJun 25 2019Jun 27 2019In this paper, we study the spectrum and the eigenvectors of radial kernels for mixtures of distributions in $\mathbb{R}^n$. Our approach focuses on high dimensions and relies solely on the concentration properties of the components in the mixture. We ... More

Spectral Properties of Radial Kernels and Clustering in High DimensionsJun 25 2019In this paper, we study the spectrum and the eigenvectors of radial kernels for mixtures of distributions in $\mathbb{R}^n$. Our approach focuses on high dimensions and relies solely on the concentration properties of the components in the mixture. We ... More

Spectral Properties of Radial Kernels and Clustering in High DimensionsJun 25 2019Jun 28 2019In this paper, we study the spectrum and the eigenvectors of radial kernels for mixtures of distributions in $\mathbb{R}^n$. Our approach focuses on high dimensions and relies solely on the concentration properties of the components in the mixture. We ... More

Orthogonal polynomials in and on a quadratic surface of revolutionJun 25 2019We present explicit constructions of orthogonal polynomials inside quadratic bodies of revolution, including cones, hyperboloids, and paraboloids. We also construct orthogonal polynomials on the surface of quadratic surfaces of revolution, generalizing ... More

Bergman kenel and oscillation theory of plurisubharmonic functionsJun 24 2019ased on Harnack's inequality and convex analysis we show that each plurisubharmonic function has bounded upper oscillation with respect to polydiscs of finite type but not for arbitrary polydiscs. As an application we obtain an approximation formula for ... More

The complex Monge-Ampère equation with a gradient termJun 24 2019We consider the complex Monge-Amp\`ere equation with an additional linear gradient term inside the determinant. We prove existence and uniqueness of solutions to this equation on compact Hermitian manifolds.

Real-analytic coordinates for smooth strictly pseudoconvex CR-structuresJun 24 2019For a smooth strictly pseudoconvex hypersurface in a complex manifold, we give a necessary and sufficient condition for being CR-diffeomorphic to a real-analytic CR manifold. Our condition amounts to a holomorphic extension property for the canonically ... More

On Gabor g-frames and Fourier series of operatorsJun 23 2019We show that Hilbert-Schmidt operators can be used to define frame-like structures for $L^2(\mathbb{R})$ over lattices in $\mathbb{R}^{2d}$ that include multi-window Gabor frames as a special case. These structures, called Gabor g-frames, are shown to ... More

Morse-type integrals on non-Kähler manifoldsJun 23 2019We pose a conjecture about Morse-type integrals in nef (1,1) classes on compact Hermitian manifolds, and we show that it holds for semipositive classes, or when the manifold admits certain special Hermitian metrics.

Theory of the Frequency Principle for General Deep Neural NetworksJun 21 2019Along with fruitful applications of Deep Neural Networks (DNNs) to realistic problems, recently, some empirical studies of DNNs reported a universal phenomenon of Frequency Principle (F-Principle): a DNN tends to learn a target function from low to high ... More

Theory of the Frequency Principle for General Deep Neural NetworksJun 21 2019Jul 02 2019Along with fruitful applications of Deep Neural Networks (DNNs) to realistic problems, recently, some empirical studies of DNNs reported a universal phenomenon of Frequency Principle (F-Principle): a DNN tends to learn a target function from low to high ... More

Cauchy-Riemann equations for free noncommutative functionsJun 21 2019In classical complex analysis analyticity of a complex function $f$ is equivalent to differentiability of its real and imaginary parts $u$ and $v$, respectively, together with the Cauchy-Riemann equations for the partial derivatives of $u$ and $v$. We ... More

Boundary value problems for general first-order elliptic differential operatorsJun 20 2019We study boundary value problems for first-order elliptic differential operators on manifolds with compact boundary. The adapted boundary operator need not be selfadjoint and the boundary condition need not be pseudo-local. We show the equivalence of ... More

Bayesian spatial clustering of extremal behaviour for hydrological variablesJun 20 2019To address the need for efficient inference for a range of hydrological extreme value problems, spatial pooling of information is the standard approach for marginal tail estimation. We propose the first extreme value spatial clustering methods which account ... More

A remark on extension of log-pluricanononical forms for nondegenerate hypersurfacesJun 19 2019We determine, complementing a paper by Marcel Morales, the log-pluricanonical forms on a nondegenerate hypersurface. This description shows that they are extendable to 1-parameter deformations. For an equisingular deformation we thus obtain a simultaneous ... More

Positivity of direct images of the relative canonical bundlesJun 19 2019Given a fibration $f$ between two projective manifolds $X$ and $Y$, we prove that $f_{\ast}(K_{X/Y}\otimes L)$ is nef, where $(L,h)$ is a pseudo-effective line bundle with mild singularity.

Free affine $\mathbb{Z}^p$-actions on ToriJun 19 2019We prove that any $\mathbb{Z}^p$-action ${\bf A}$ that acts by automorphisms of $\mathbb{Z}^q$ with a non-zero fixed-point set induces a unipotent factor of the $\mathbb{Z}^p$-action ${\bf A}$ which determines whether the action ${\bf A}$ is {\it liberated ... More

Coherent States for the Manin Plane via Toeplitz QuantizationJun 18 2019In the theory of Toeplitz quantization of algebras, as developed by the second author, coherent states are defined as eigenvectors of a Toeplitz annihilation operator. These coherent states are studied in the case when the algebra is the generically non-commutative ... More

Holomorphic one-forms without zeros on threefoldsJun 18 2019We show that a smooth complex projective threefold admits a holomorphic one-form without zeros if and only if the underlying real 6-manifold fibres smoothly over the circle, and we give a complete classification of all threefolds with that property. Our ... More

Zeros of holomorphic one-forms and topology of Kähler manifoldsJun 18 2019A conjecture of Kotschick predicts that a compact K\"ahler manifold $X$ fibres smoothly over the circle if and only if it admits a holomorphic one-form without zeros. In this paper we develop an approach to this conjecture and verify it in dimension two. ... More

A twin error gauge for Kaczmarz's iterationsJun 18 2019We propose two new methods based on Kaczmarz's method that produce a regularized solution to noisy tomography problems. These methods exhibit semi-convergence when applied to inverse problems, and the aim is therefore to stop near the semi-convergence ... More

On a generalization of Inoue and Oeljeklaus-Toma manifoldsJun 18 2019In this paper we construct a family of complex analytic manifolds that generalize Inoue surfaces and Oeljeklaus-Toma manifolds. To a matrix $M$ in $SL(N,\mathbb{Z})$ satisfying some mild conditions on its characteristic polynomial we associate a manifold ... More

A Kollár-type vanishing theoremJun 18 2019Jun 19 2019Let $f:X\rightarrow Y$ be a smooth fibration between two complex manifolds $X$ and $Y$, and let $L$ be a pseudo-effective line bundle on $X$. We obtain a sufficient condition for $R^{q}f_{\ast}(K_{X/Y}\otimes L)$ to be reflexive and hence derive a Koll\'{a}r-type ... More

Parametric and non-parametric estimation of extreme earthquake event: the joint tail inference for mainshocks and aftershocksJun 17 2019In an earthquake event, the combination of a strong mainshock and damaging aftershocks is often the cause of severe structural damages and/or high death tolls. The objective of this paper is to provide estimation for the probability of such extreme events ... More

Local and Global Homogeneity for Manifolds of Positive CurvatureJun 15 2019In this note we study globally homogeneous Riemannian quotients $\Gamma\backslash (M,ds^2)$ of homogeneous Riemannian manifolds $(M,ds^2)$. The Homogeneity Conjecture is that $\Gamma\backslash (M,ds^2)$ is (globally) homogeneous if and only if $(M,ds^2)$ ... More

Local and Global Homogeneity for Manifolds that admit a Positive Curvature MetricJun 15 2019Jul 03 2019In this note we study globally homogeneous Riemannian quotients $\Gamma\backslash (M,ds^2)$ of homogeneous Riemannian manifolds $(M,ds^2)$. The Homogeneity Conjecture is that $\Gamma\backslash (M,ds^2)$ is (globally) homogeneous if and only if $(M,ds^2)$ ... More

Dimension Reduction and Kernel Principal Component AnalysisJun 15 2019We study non-linear data-dimension reduction. We are motivated by the classical linear framework of Principal Component Analysis. In nonlinear case, we introduce instead a new kernel-Principal Component Analysis, manifold and feature space transforms. ... More

Four beautiful quadrature rulesJun 14 2019A framework is presented to compute approximations of an integral $I(f)=\displaystyle \int_a^b f(x) dx$ from a pair of companion rules and its associate rule. We show that an associate rule is a weighted mean of two companion rules. In particular, the ... More

Fibred algebraic surfaces and commutators in the Symplectic groupJun 13 2019We describe the minimal number of critical points and the minimal number $s$ of singular fibres for a non isotrivial fibration of a surface $S$ over a curve $B$ of genus $1$, constructing a fibration with $s=1$ and irreducible singular fibre with $4$ ... More

Global branches of solutions for a class of non uniformly fully nonlinear elliptic equationsJun 13 2019We consider singular perturbations of eigenvalue problems. We prove that to these problems correspond simple eigenvalues and we study their asymptotic behavior. As a result, we prove global bifurcation results for non uniformly and fully nonlinear elliptic ... More

Combinatorially equivalent hyperplane arrangementsJun 13 2019We study the combinatorics of hyperplane arrangements over arbitrary fields. Specifically, we determine in which situation an arrangement and its reduction modulo a prime number have isomorphic lattices via the use of minimal strong $\sigma$-Gr\"obner ... More

Fast, reliable and unrestricted iterative computation of Gauss--Hermite and Gauss--Laguerre quadraturesJun 12 2019Methods for the computation of classical Gaussian quadrature rules are described which are effective both for small and large degree. These methods are reliable because the iterative computation of the nodes has guaranteed convergence, and they are fast ... More

Tensor train optimization for mathematical model of social networksJun 12 2019The optimization algorithms for solving multi-parameter inverse problem for the mathematical model of parabolic equations arising in social networks, epidemiology and economy are investigated. The data fitting is formulated as optimization of least squares ... More

Torus computed tomographyJun 12 2019We present a new computed tomography (CT) method for inverting the Radon transform in 2D. The idea relies on the geometry of the flat torus, hence we call the new method Torus CT. We prove new inversion formulas for integrable functions, solve a minimization ... More

Dynamics of singular complex analytic vector fields with essential singularities IIJun 10 2019Generically, the singular complex analytic vector fields $X$ on the Riemann sphere $\widehat{\mathbb{C}}_{z}$ belonging to the family $$ \mathscr{E}(r,d)=\Big\{ X(z)=\frac{1}{P(z)}\ \text{e}^{E(z)}\frac{\partial}{\partial z} \ \big\vert \ P, E\in\mathbb{C}[z], ... More

Algebraic Overshear Density PropertyJun 10 2019We introduce the notion of the algebraic overshear density property which implies both the algebraic notion of flexibility and the holomorphic notion of the density property. We investigate basic consequences of this stronger property, and propose further ... More

Bounded $H_{\infty}$-calculus for Boundary Value Problems on Manifolds with Conical SingularitiesJun 09 2019Realizations of differential operators subject to differential boundary conditions on manifolds with conical singularities are shown to have a bounded $H_\infty$-calculus in appropriate $L_p$-Sobolev spaces provided suitable conditions of parameter-ellipticity ... More

Decomposition of the tensor product of two Hilbert modulesJun 09 2019Given a pair of positive real numbers $\alpha, \beta$ and a sesqui-analytic function $K$ on a bounded domain $\Omega \subset \mathbb C^m$, in this paper, we investigate the properties of the sesqui-analytic function $\mathbb K^{(\alpha, \beta)}:= K^{\alpha+\beta}\big(\partial_i\bar{\partial}_j\log ... More

A Note on the Bateman-Horn ConjectureJun 08 2019We report the results of our empirical investigations on the Bateman-Horn conjecture. This conjecture, in its commonly known form, produces rather large deviations when the polynomials involved are not monic. We propose a modified version of the conjecture ... More

Carleman approximation by conformal minimal immersions and directed holomorphic curvesJun 07 2019Let $\mathcal{R}$ be an open Riemann surface. In this paper we prove that every continuous function $M \to \mathbb{R}^n$, $n\ge 3$, defined on a divergent Jordan arc $M \subset \mathcal{R}$ can be approximated in the Carleman sense by conformal minimal ... More

Congruences on Orthogonal Rook Monoids and Symplectic Rook MonoidsJun 07 2019We give a complete classification of all nonuniform congruences on orthogonal rook monoids and symplectic rook monoids. We find that there are four kinds of nonuniform congruences on the orthogonal rook monoids ${OR}_n$ for even $n\ne 4$, and we describe ... More

Hardy-space function theory, operator model theory, and dissipative linear systems: the multivariable, free-noncommutative, weighted Bergman-space settingJun 06 2019Jun 10 2019It is known that (i) a subspace ${\mathcal N}$ of the Hardy space $H^2$ which is invariant under the backward shift operator can be represented as the range of the observability operator of a conservative discrete-time linear system, (ii) the transfer-function ... More

Hardy-space function theory, operator model theory, and dissipative linear systems: the multivariable, free-noncommutative, weighted Bergman-space settingJun 06 2019It is known that (i) a subspace ${\mathcal N}$ of the Hardy space $H^2$ which is invariant under the backward shift operator can be represented as the range of the observability operator of a conservative discrete-time linear system, (ii) the transfer-function ... More

Families of Supermanifolds: Splitting Types and Obstruction MapsJun 06 2019In this article we study the notion of supermanifolds families, starting from Green's general classification of supermanifolds. The topics studied divide this article into two distinct parts, labelled I and II respectively. Part I concerns the splitting ... More

A neural network based policy iteration algorithm with global $H^2$-superlinear convergence for stochastic games on domainsJun 05 2019In this work, we propose a class of numerical schemes for solving semilinear Hamilton-Jacobi-Bellman-Isaacs (HJBI) boundary value problems which arise naturally from exit time problems of diffusion processes with controlled drift. We exploit policy iteration ... More

Holomorphic functions with large cluster setsJun 05 2019We study linear and algebraic structures in sets of bounded holomorphic functions on the ball which have large cluster sets at every possible point (i.e., every point on the sphere in several complex variables and every point of the closed unit ball of ... More

Analytic Solutions of the Heat EquationJun 05 2019Motivated by the recent proof of Newman's conjecture \cite{R-T} we study certain properties of entire caloric functions, namely solutions of the heat equation $\partial_t F = \partial_z^2 F$ which are entire in $z$ and $t$. As a prerequisite, we establish ... More

Analytic Solutions of the Heat EquationJun 05 2019Jun 08 2019Motivated by the recent proof of Newman's conjecture \cite{R-T} we study certain properties of entire caloric functions, namely solutions of the heat equation $\partial_t F = \partial_z^2 F$ which are entire in $z$ and $t$. As a prerequisite, we establish ... More

Non-existence of orthogonal complex structures on the round 6-sphereJun 05 2019In this short note, we review the well-known result that there is no orthogonal complex structure on the 6-sphere with respect to the round metric.

Single-cylinder square-tiled surfaces and the ubiquity of ratio-optimising pseudo-AnosovsJun 05 2019In every connected component of every stratum of Abelian differentials, we construct square-tiled surfaces with one vertical and one horizontal cylinder. We show that for all but the hyperelliptic components this can be achieved in the minimum number ... More

Locally Heavy Hyperplanes in MultiarrangementsJun 05 2019Hyperplane Arrangements of rank $3$ admitting an unbalanced Ziegler restriction are known to fulfil Terao's conjecture. This long-standing conjecture asks whether the freeness of an arrangement is determined by its combinatorics. In this note we prove ... More

Geometric formalities along the Chern-Ricci flowJun 04 2019In this paper, we study how the notions of geometric formality according to Kotschick and other geometric formalities adapted to the Hermitian setting evolve under the action of the Chern-Ricci flow on class VII surfaces, including Hopf and Inoue surfaces, ... More

New solution of a problem of Kolmogorov on width asymptotics in holomorphic function spacesJun 03 2019Given a domain $D$ in $\mathbb{C}^n$ and $K$ a compact subset of $D$, the set $\mathcal{A}_K^D$ of all restrictions of functions holomorphic on $D$ the modulus of which is bounded by $1$ is a compact subset of the Banach space $C(K)$ of continuous functions ... More

On equivalence problem of 2-nondegenerate CR geometries with simple modelsJun 03 2019Let $G$ be a simple Lie group and $H$ a Lie subgroup of $G$. We determine when the homogeneous space $G/H$ is a maximally symmetric model of a 2--nondegenerate CR geometry. In particular, we solve the equivalence problem for 2--nondegenerate CR geometries ... More