Related papers: Uniform parameterization of subanalytic sets and d…

We study systems of polynomial equations in infinite finitely generated commutative associative rings with an identity element. For each such ring $R$ we obtain an interpretation by systems of equations of a ring of integers $O$ of a finite…

We prove that the number of distinct homotopy types of limits of one-parameter semi-algebraic families of closed and bounded semi-algebraic sets is bounded singly exponentially in the additive complexity of any quantifier-free first order…

Higher-order unification has been shown to be undecidable. Miller discovered the pattern fragment and subsequently showed that higher-order pattern unification is decidable and has most general unifiers. We extend the algorithm to…

Conformal mapping, a classical topic in complex analysis and differential geometry, has become a subject of great interest in the area of surface parameterization in recent decades with various applications in science and engineering.…

We prove the equivalence between geometric and analytic definitions of quasiconformality for a homeomorphism $f\colon X\rightarrow Y$ between arbitrary locally finite separable metric measure spaces, assuming no metric hypotheses on either…

A central question in random matrix theory is universality. When an emergent phenomena is observed from a large collection of chosen random variables it is natural to ask if this behavior is specific to the chosen random variable or if the…

Dimensional regularization of Euclidean momentum space integrals is a highly successful technique in renormalization of quantum field theories. While it yields a straightforward algorithmic method, with which to evaluate diagrams beyond…

We consider principled alternatives to unsupervised learning in data mining by situating the learning task in the context of the subsequent analysis task. Specifically, we consider a query-answering (hypothesis-testing) task: In the…

We use the recently established existence and regularity of area and energy minimizing discs in metric spaces to obtain canonical parametrizations of metric surfaces. Our approach yields a new and conceptually simple proof of a well-known…

The notion of $c$-differential uniformity has recently received a lot of attention since its proposal~\cite{Ellingsen}, and recently a characterization of perfect $c$-nonlinear functions in terms of difference sets in some quasigroups was…

A classical result in the theory of Loewner's parametric representation states that the semigroup $\mathfrak U_*$ of all conformal self-maps $\phi$ of the unit disk $\mathbb{D}$ normalized by $\phi(0) = 0$ and $\phi'(0) > 0$ can be obtained…

Let $\zeta$ be a real transcendental number. We introduce a new method to find upper bounds for the classical exponent $\widehat{w}_{n}(\zeta)$ concerning uniform polynomial approximation. Our method is based on the parametric geometry of…

We prove a Zalcman-Pang lemma in several complex variables and apply it to obtain several complex variables analogues of the known normality criteria like Lappan's five-point theorem and Schwick's theorem.

In recent years, we have seen several approaches to the graph isomorphism problem based on "generic" mathematical programming or algebraic (Gr\"obner basis) techniques. For most of these, lower bounds have been established. In fact, it has…

This article introduces Hilbert $*$-categories: an abstraction of categories with similar algebraic and analytic properties to the categories of real, complex, and quaternionic Hilbert spaces and bounded linear maps. Other examples include…

In a prior paper \cite{EFRST20}, two of us, along with P. Ellingsen, P. Felke and A. Tkachenko, 1defined a new (output) multiplicative differential, and the corresponding $c$-differential uniformity, which has the potential of extending…

We propose a method for inferring \emph{parameterized regular types} for logic programs as solutions for systems of constraints over sets of finite ground Herbrand terms (set constraint systems). Such parameterized regular types generalize…

We prove that a family of quasiregular mappings of a domain $\Omega$ which are uniformly bounded in $L^p$ for some $p>0$ form a normal family. From this we show how an elliptic estimate on a functional differences implies all directional…

UNIFORM algebras have been extensively investigated because of their importance in the theory of uniform approximation and as examples of complex Banach algebras. An interesting question is whether analogous algebras exist when a complete…

It is, by now, classical that lattices in higher rank semisimple groups have various rigidity properties. In this work, we add another such rigidity property to the list: uniform stability with respect to the family of unitary operators on…