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We show a general theorem of existence of temporal foliations in a general causal set, under mild constraints. Then we study automorphisms of infinite causal sets (which satisfy further requirements) and show that they fall under one of two…
Graphical models are a key class of probabilistic models for studying the conditional independence structure of a set of random variables. Circular variables are special variables, characterized by periodicity, arising in several contexts…
We deal with the algebraicity of an iterated Puiseux series in several variables in terms of the properties of its coefficients. Our aim is to generalize to several variables the results from [HM15]. We show that the algebraicity of such a…
Let $F(x, y)$ be a binary form of degree at least three and non-zero discriminant. In this article we compute the automorphism group $\operatorname{Aut} F$ for four families of binary forms. The first two families that we are interested in…
We study the ring generated over a field of characteristic 0 by noncommuting indeterminates {x_1,x_2,...,x_n} subject only to the relations x_i\sigma_k=\sigma_k x_i, for i,k=1,2,...,n, and their consequences, where \sigma_k…
We outline the proof of a conjecture of Kontsevich on the isomorphism between the group of polynomial symplectomorphisms in $2n$ variables and the group of automorphisms of the $n$-th Weyl algebra over complex numbers. Our proof uses…
We prove that the super-linearizability of polynomial systems is preserved by all currently known classes of polynomial automorphisms of $\R^n$. We then establish connections between such automorphisms and a sufficient condition for…
The groups of automorphisms of the Lie algebras of unitriangular polynomial derivations are found.
The analysis of observable phenomena (for instance, in biology or physics) allows the detection of dynamical behaviors and, conversely, starting from a desired behavior allows the design of objects exhibiting that behavior in engineering.…
We summarize researches - in great deal jointly with my host Y. Sarantopoulos and his PhD. students V. Anagnostopoulos and A. Pappas - started by a Marie Curie fellowship in 2001 and is still continuing. The project was to study…
Let $k$ be an arbitrary field of characteristic 0. We prove that the group of automorphisms of a free Poisson field $P(x,y)$ in two variables $x,y$ over $k$ is isomorphic to the Cremona group $\mathrm{Cr}_2(k)$. We also prove that the…
In these notes we investigate the rings of real polynomials in four variables, which are invariant under the action of the reflectiongroups [3,4,3] and [3,3,5]. It is well known that they are rationally generated in degree 2,6,8,12 and…
We prove p-adic functoriality for inner forms of unitary groups in three variables by establishing the existence of morphisms between eigenvarieties that extend the classical Langlands functoriality.
We study the shape of the probability mass function of the Markov binomial distribution, and give necessary and sufficient conditions for the probability mass function to be unimodal, bimodal or trimodal. These are useful to analyze the…
In this article we generalize a theorem of Benson for generalized quadrangles to strongly regular graphs and directed strongly regular graphs. The main result provides numerical restrictions on the number of fixed vertices and the number of…
We introduce horizontal and vertical motivic invariants of birational maps between rational dominant maps and study their basic properties. As a first application, we show that the (usual) motivic invariants vanish for birational…
We generally study the density of eigenvalues in unitary ensembles of random matrices from the recurrence coefficients with regularly varying conditions for the orthogonal polynomials. First we calculate directly the moments of the density.…
We use a simple description of the outer automorphism of S_6 to cleanly describe the invariant theory of six points in P^1, P^2, and P^3.
A four dimensional generally covariant field theory is presented which describes non-dynamical three geometries coupled to scalar fields. The theory has an infinite number of physical observables (or constants of the motion) which are…
The multivariate integer Chebyshev problem is to find polynomials with integer coefficients that minimize the supremum norm over a compact set in $\C^d.$ We study this problem on general sets, but devote special attention to product sets…