Related papers: Differential Weil Descent and Differentially Large…
We prove that the (elementary) class of differential-difference fields in characteristic $p>0$ admits a model-companion. In the terminology of Chatzidakis-Pillay, this says that the class of differentially closed fields of characteristic…
The purpose of this paper is to combine classical methods from transcendental number theory with the technique of restriction to real scalars. We develop a conceptual approach relating transcendence properties of algebraic groups to results…
This paper introduces the notion of a derived splinter. Roughly speaking, a scheme is a derived splinter if it splits off from the coherent cohomology of any proper cover. Over a field of characteristic 0, this condition characterises…
Under reasonable assumptions about the complex structure of the set of singularities on the Coulomb branch of $\mathcal N=2$ superconformal field theories, we present a relatively simple and elementary argument showing that the scaling…
Descent theory for linear categories is developed. Given a linear category as an extension of a diagonal category, we introduce descent data, and the category of descent data is isomorphic to the category of representations of the diagonal…
We present a survey on Weil sums in which an additive character of a finite field $F$ is applied to a binomial whose individual terms (monomials) become permutations of $F$ when regarded as functions. Then we indicate how these Weil sums…
We establish new uniform height inequalities for rational points on higher-dimensional varieties, extending the classical Roth-Schmidt-Subspace paradigm to the Arakelov-theoretic setting. Our main result provides sharp bounds for heights…
Let $T$ be a polynomially bounded o-minimal theory extending the theory of real closed ordered fields. Let $K$ be a model of $T$ equipped with a $T$-convex valuation ring and a $T$-derivation. If this derivation is continuous with respect…
Starting from the classic contraction mapping principle, we establish a general, flexible, variational setting that turns out to be applicable to many situations of existence in Differential Equations. We show its potentiality with some…
Large deviation principles and related results are given for a class of Markov chains associated to the "leaves" in random recursive trees and preferential attachment random graphs, as well as the "cherries" in Yule trees. In particular,…
As an example of what happens with physically relevant theories like effective gravity, we consider the covariant relativistic theory of a scalar field of arbitrarily higher differential order. A procedure based on the Legendre…
We establish the first global results for groups definable in tame expansions of o-minimal structures. Let $\mathcal N$ be an expansion of an o-minimal structure $\mathcal M$ that admits a good dimension theory. The setting includes dense…
The classical Clarke subdifferential alone is inadequate for understanding automatic differentiation in nonsmooth contexts. Instead, we can sometimes rely on enlarged generalized gradients called "conservative fields", defined through the…
In this paper, we establish a large deviation principle for stochastic evolution equations with reflection in an infinite dimensional ball. Weak convergence approach plays an important role.
Being closed under truncation for subsets of generalized series fields is a robust property in the sense that it is preserved under various algebraic and transcendental extension procedures. Nevertheless, in Chapter 4 of this dissertation,…
Large deviations for sums of i.i.d.\ random variables with stretched-exponential tails (also called Weibull or semi-exponential tails) have been well understood since the 60's, going back to Nagaev's seminal work. Many extensions in the…
In this paper we introduce the classical and quantum covariant Weil algebras. Covariant Weil algebras are simultaneous generalizations of Weil algebras and family algebras. We will define differentials, Lie derivatives and contractions on…
We initiate a study on a range of new generalized derivations of finite-dimensional Lie algebras over an algebraically closed field of characteristic zero. This new generalization of derivations has an analogue in the theory of associative…
The differential representation is a novel formalism for studying boundary correlators in $(d+1)$-dimensional anti-de Sitter space. In this letter, we generalize the differential representation beyond tree level using the notion of…
We study the behaviour of differential forms in a manifold having at least one of their maximal isotropic local distributions endowed with the special algebraic property of being decomposable. We show that they can be represented as the sum…