Related papers: Integration and Cell Decomposition in $P$-minimal …

Let $T$ be a complete, model-complete, geometric dp-minimal $\mathcal{L}$-theory of topological fields of characteristic $0$ and let $T(\partial)$ be the theory of expansions of models of $T$ by a derivation $\partial$. We assume that…

It is hereby established that the set of Lipschitz functions $f:\mathcal{U}\rightarrow \mathbb{R}$ ($\mathcal{U}$ nonempty open subset of $\ell_{d}^{1}$) with maximal Clarke subdifferential contains a linear subspace of uncountable…

In this article we give strong versions for preparation theorems for $\mathbb{R}_{an,exp}$-definable functions outgoing from methods of Lion and Rolin ($\mathbb{R}_{an,exp}$ is the o-minimal structure generated by all restricted analytic…

In this paper we complete the description of the $B\mathbb{Z} /p$-cellularization of the classifying spaces of all finite groups, for all primes $p$. The techniques are based in a careful analysis of the $p$-fusion structure of the groups…

We consider classes $ \mathcal{A}_M(S) $ of functions holomorphic in an open plane sector $ S $ and belonging to a strongly non-quasianalytic class on the closure of $ S $. In $ \mathcal{A}_M(S) $, we construct functions which are flat at…

Let $(R, \mf, k_R)$ be regular local $k$-algebra satisfying the weak Jacobian criterion, such that $k_R/k$ is an algebraic field extension. Let $D_R$ be the ring of $k$-linear differential operators of $R$. We give an explicit decomposition…

Let k be an algebraically closed field and A a finite dimensional associative k-algebra. We prove that there is no gap in the lengths of indecomposable A-modules of finite length. The analogous result holds for an abelian k-linear category…

We present an algorithm which produces a decomposition of a regular cellular complex with a discrete Morse function analogous to the Morse-Smale decomposition of a smooth manifold with respect to a smooth Morse function. The advantage of…

In this paper, we give a complete description of the deformation classes of real structures on minimal ruled surfaces. In particular, we show that these classes are determined by the topology of the real structure, which means that real…

The paper deals with Henselian valued field with analytic structure. Actually, we are focused on separated analytic structures, but the results remain valid for strictly convergent analytic ones as well. A classical example of the latter is…

We prove two structure theorems for simple, locally finite dimensional Lie algebras over an algebraically closed field of characteristic $p$ which give sufficient conditions for the algebras to be of the form $[R^{(-)}, R^{(-)}] / (Z(R)…

Let $R$ be a unitary commutative real algebra and $K\subseteq Hom(R,\mathbb{R})$, closed with respect to the product topology. We consider $R$ endowed with the topology $\mathcal{T}_K$, induced by the family of seminorms…

Let $\widetilde{\mathcal M}=\langle \mathcal M, P\rangle$ be an expansion of an o-minimal structure $\mathcal M$ by a dense set $P\subseteq M$, such that three tameness conditions hold. We prove that the induced structure on $P$ by…

Every bounded definable open set is a union of finitely many open strong cells in a weakly o-minimal expansion of a real closed field. We prove this fact and another theorem similar to it.

We extend the shell and kernel reductions for hyperexponential functions over the field of rational functions to a monomial extension. Both of the reductions are incorporated into one algorithm. As an application, we present an additive…

We develop the theory of algebraic groups over real closed fields and apply the results to construct a geometric object $\mathcal{B}$ and to prove that $\mathcal{B}$ is an affine $\Lambda$-building. We use a model theoretic transfer…

Given a Lie group G whose Lie algebra is endowed with a nondegenerate invariant symmetric bilinear form, we construct a Poisson algebra of continuous functions on a certain open subspace R of the space of representations in G of the…

We describe a class of sharply o-minimal structures, called analytically generated structures, whose definable sets and their complexity filtration are determined by the collection of definable complex cells. We prove a polynomially…

A closed geodesic on the modular surface is "low-lying" if it does not travel "high" into the cusp. It is "fundamental" if it corresponds to an element in the class group of a real quadratic field. We prove the existence of infinitely many…

Given primes $\ell\ne p$, we record here a $p$-adic valued Fourier theory on a local field over $\mathbf{Q}_\ell$, which is developed under the perspective of group schemes. As an application, by substituting rigid analysis for complex…