Related papers: Global pluripotential theory over a trivially valu…
In this work we consider infinite dimensional extensions of some finite dimensional Gaussian geometric functionals called the Gaussian Minkowski functionals. These functionals appear as coefficients in the probability content of a tube…
We introduce a sheaf theoretic viewpoint on functional analysis designed for infinite dimensional Lie group actions. We develop functional calculus for Banach valued functors and, in particular, prove the existence of an exponential map for…
We develop a theory of vector-valued heights and intersections defined relative to finitely generated extensions K/k. These generalize both number field and geometric heights. When k is Q or F_p, or when a non-isotriviality condition holds,…
By seeing whether a Liouville type theorem holds for positive, bounded, and/or finite energy $p$-harmonic and $p$-quasiharmonic functions, we classify proper metric spaces equipped with a locally doubling measure supporting a local…
We revisit and connect several notions of algebraic multiplicities of zeros of analytic operator-valued functions and discuss the concept of the index of meromorphic operator-valued functions in complex, separable Hilbert spaces.…
Observable structures of a topological field theory of AKSZ type are analyzed. From a double (or multiple) complex structure of observable algebras, new topological invariants are constructed. Especially, Donaldson polynomial invariants and…
We use the theory of fully matricial, or non-commutative, functions to investigate infinite divisibility and limit theorems in operator-valued non-commutative probability. Our main result is an operator-valued analogue of the Bercovici-Pata…
In a series of recent papers, a harmonic and hypercomplex function theory in superspace has been established and amply developed. In this paper, we address the problem of establishing Cauchy integral formulae in the framework of Hermitian…
We present a central extension of the $(m,n)$ super-Poincar\'e algebra in two dimensions. Besides the usual Poincar\'e generators and the $(m,n)$ supersymmetry generators we have $(m,n)$ Grassmann generators, a bosonic internal symmetry…
An examples of Monge-Ampere equations connected with six-dimensional generalization of the Plebanski four-dimensional space are considered. Their particular solutions are constructed.
We study infinite tree and ultrametric matrices, and their action on the boundary of the tree. For each tree matrix we show the existence of a symmetric random walk associated to it and we study its Green potential. We provide a…
We consider maps into Riemannian manifolds of non-positive curvature and start developing a systematic PDE theory. We control the Sobolev $H^{2,2}$-norm of such a map in terms of its energy, the $L^2$-norm of its tension field and a…
Metric theories of gravity are studied, beginning with a general action that is quadratic in curvature and allows infinite inverse powers of the d'Alembertian operator, resulting in infrared non-local extensions of general relativity. The…
A natural extension of the Dijkgraaf-Vafa proposal is to include fields in the fundamental representation of the gauge group. In this paper we use field theory techniques to analyze gauge theories whose tree level superpotential is a…
This is the second paper in a series of investigations of the pluripotential theory on Teichm\"uller space. The main purpose of this paper is to establish the Poisson integral formula for pluriharmonic functions on Teichm\"uller space which…
In this paper we study finite dimensional algebras, in particular finite semifields, through their correspondence with nonsingular threefold tensors. We introduce a alternative embedding of the tensor product space into a projective space.…
We introduce an extension of interpolation theory to more than two spaces by employing a functional parameter, while retaining a fully functorial and systematic framework. This approach allows for the construction of generalized…
In this paper we generalize the Ritt-Kolchin method of characteristic sets and the classical Gr\"obner basis technique to prove the existence and obtain methods of computation of multivariate difference-differential dimension polynomials…
We begin by defining general hypergeometric functions over finite fields and obtaining a finite field analogue of a classical symmetry in their complex counterparts. We give a geometric proof for the symmetry by constructing isomorphisms…
We consider the topological theory of Witten type for gauge differential p-forms. It is shown that some topological invariants such as linking numbers appear under quantization of this theory. The non-abelian generalization of the model is…