Related papers: Inverse Function Theorems for Arc-analytic Homeomo…

Semilinear maps are a generalization of linear maps between vector spaces where we allow the scalar action to be twisted by a ring homomorphism such as complex conjugation. In particular, this generalization unifies the concepts of linear…

The notion of supershift (in itself a generalization of the notion of superoscillation arising in quantum mechanics) expresses the fact that the sampling of a function in an interval allows to compute the values of the function far from the…

We study biorthogonal sequences with special properties, such as weak or weak-star convergence to 0, and obtain an extension of the Josefson-Nissenzweig theorem. This result is applied to embed analytic disks in the fiber over 0 of the…

We study one variable meromorphic functions mapping a planar real algebraic set $A$ to another real algebraic set in the complex plane. By using the theory of Schwarz reflection functions, we show that for certain $A$, these meromorphic…

We extend Baumgartner's result on isomorphisms of aleph_1 dense subsets of the reals R in two ways: First, the function can be made to be absolutely continuous. Second, one can replace R by R^n.

Let $\phi: A\to A$ be a (not necessarily linear, additive or continuous) map of a standard operator algebra. Suppose for any $a,b\in A$ there is an algebra automorphism $\theta_{a,b}$ of $ A$ such that \begin{align*} \phi(a)\phi(b) =…

We give a new proof of the rectilinearization theorem of Hironaka. We deduce rectilinearization as a consequence of our theorem on local monomialization for complex and real analytic morphisms.

Two blow-analytically equivalent real analytic plane function germs are sub-analytically bi-Lipschitz contact equivalent

Let $L$ be an algebra over a field $F$ with the binary operations $+$ and $[,]$. Then $L$ is called a left Leibniz algebra if it satisfies the left Leibniz identity: $[[a,b],c]=[a,[b,c]]-[b,[a,c]]$ for all elements $a,b,c\in L$. The…

We study singular real analytic Levi-flat subsets invariant by singular holomorphic foliations in complex projective spaces. We give sufficient conditions for a real analytic Levi-flat subset to be the pull-back of a semianalytic Levi-flat…

Fintushel and Stern defined the rational blow-down construction [FS] for smooth 4-manifolds, where a linear plumbing configuration of spheres $C_n$ is replaced with a rational homology ball $B_n$, $n \geq 2$. Subsequently, Symington [Sy]…

In this article we prove that every germ of analytic meromorphic function at $(\mathbb{C}^{2},0)$ is equivalent, under the right composition by a germ of biholomorphism, to a germ of algebraic meromorphic function. An analogous result is…

In this paper we give a geometric description of the foliation of a generic real analytic family unfolding a real analytic vector field with a weak focus at the origin, and show that two such families are orbitally analytically equivalent…

By an influential theorem of Boman, a function $f$ on an open set $U$ in $\mathbb R^d$ is smooth ($\mathcal C^\infty$) if and only if it is arc-smooth, i.e., $f\circ c$ is smooth for every smooth curve $c : \mathbb R \to U$. In this paper…

The first part of this article is devoted to the study families of totally real intersecting $n$-submanifolds of $(\Bbb C^n,0)$. We give some conditions which allow to straighten holomorphically the family. If this is not possible to do it…

Consider a homeomorphism $f$ defined on a compact metric space $X$ and a continuous map $\phi\colon X \to \mathbb{R}$. We provide an abstract criterion, called \emph{control at any scale with a long sparse tail} for a point $x\in X$ and the…

In this talk, we show how the Connes-Kreimer Hopf algebra morphism can be extended when taking into account the wave-function renormalization. This leads us to a semi-direct product of invertible power series by formal diffeomorphisms.

Let $U$ be an open relatively compact subanalytic subset of a real analytic manifold. We show that there exists a finite linear covering (in the sense of Guillermou and Schapira) of $U$ by subanalytic open subsets of $U$ homeomorphic to a…

A numbering of a countable family $S$ is a surjective map from the set of natural numbers $\omega$ onto $S$. A numbering $\nu$ is reducible to a numbering $\mu$ if there is an effective procedure which given a $\nu$-index of an object from…

Let $(f, g)$ be a pair of complex analytic functions on a singular analytic space $X$. We give ``the correct'' definition of the relative polar curve of $(f, g)$, and we give a very formal generalization of L\^e's attaching result, which…