Related papers: Polydisc version of Arveson's conjecture

This is our sequel to our previous work on the corresponding generalized Frobenius modules over some big multivariate Robba rings. We will go beyond our previous discussion where we focused on the corresponding analytic functions on…

Let $\Omega \subset \mathbb{C}^m$ be an open, connected and bounded set and $\mathcal{A}(\Omega)$ be a function algebra of holomorphic functions on $\Omega$. In this article we study quotient Hilbert modules obtained from submodules,…

We consider the system of $N$ ($\ge2$) hard disks of masses $m_1,...,m_N$ and radius $r$ in the flat unit torus $\Bbb T^2$. We prove the ergodicity (actually, the B-mixing property) of such systems for almost every selection…

We extend the polydisk theorem of [21], originally established for classical Cartan-Hartogs domains, to Hartogs domains over arbitrary (possibly reducible and exceptional) bounded symmetric domains. We further establish a dual counterpart…

Let (E,D,P) be a flat vector bundle with a parabolic structure over a punctured Riemann surface, (M,g). We consider a deformation of the harmonic metric equation which we call the Poisson metric equation. This equation arises naturally as…

Here we construct spaces of coinvariants for Heisenberg vertex algebras on abelian varieties and show that these globalize to twisted $\mathscr{D}$-modules on the moduli space of abelian varieties. Remarkably, we recover the standard…

We show that the dualizing sheaves of reduced simple normal crossings pairs have a canonical weight filtration in a compatible way with the one on the corresponding mixed Hodge modules by calculating the extension classes between the…

A polyhedron $\textbf{P} \subset \mathbb{R}^3$ has Rupert's property if a hole can be cut into it, such that a copy of $\textbf{P}$ can pass through this hole. There are several works investigating this property for some specific polyhedra:…

We study Hodge Integrals on Moduli Spaces of Admissible Covers. Motivation for this work comes from Bryan and Pandharipande's recent work on the local GW theory of curves, where analogouos intersection numbers, computed on Moduli Spaces of…

We consider Arveson's problem on the maximality of subdiagonal algebras. We prove that a subdiagonal algebra is maximal if it is invariant under the modular group of a faithful normal state which is preserved by the conditional expectation…

We prove many cases of a conjecture of Buzzard, Diamond and Jarvis on the possible weights of mod $p$ Hilbert modular forms, by making use of modularity lifting theorems and computations in $p$-adic Hodge theory.

This article provides a thorough investigation into Gilbert's Conjecture, pertaining to Hardy spaces in the upper half-space valued in Clifford modules. We explore the conjecture proposed by Gilbert in 1991, which seeks to extend the…

Motivated by classical Alexander invariants of affine hypersurface complements, we endow certain finite dimensional quotients of the homology of abelian covers of complex algebraic varieties with a canonical and functorial mixed Hodge…

In this paper we give a version of Krivine-Stengle's Positivstellensatz, Schweighofer's Positivstellensatz, Scheiderer's local-global principle, Scheiderer's Hessian criterion and Marshall's boundary Hessian conditions for polynomial…

We study the orthogonal projection of homogeneous polynomials onto the space of homogeneous polyharmonic polynomials. To do this we derive the decomposition of homogeneous polynomials in terms of the Kelvin transform of derivatives of the…

We introduce a supporting combinatorial framework for the Flat Wall Theorem. In particular, we suggest two variants of the theorem and we introduce a new, more versatile, concept of wall homogeneity as well as the notion of regularity in…

Hadwiger's theorem is a Helly-type theorem involving common transversals to families of convex sets instead of common intersections. Subsequently, Pollack and Wenger identified a necessary and sufficient condition, called a consistent…

We consider symmetric (under the action of products of finite symmetric groups) real algebraic varieties and semi-algebraic sets, as well as symmetric complex varieties in affine and projective spaces, defined by polynomials of degrees…

\begin{abstract} In this paper, we partly solve the generalized Khavinson conjecture in the setting of hyperbolic harmonic mappings in Hardy space. Assume that $u=\mathcal{P}_{\Omega}[\phi]$ and $\phi\in L^{p}(\partial\Omega, \mathbb{R})$,…

In this article, we give a condition on the vanishing of finitely many homogeneous components which must imply the asymptotic vanishing for multigraded modules. We apply our result to multi-Rees algebras of ideals. As a consequence, we…