Related papers: On the infinitary van der Waerden Theorem
Our goal in the present paper is to give a new ergodic proof of a well-known Veech's result, build upon our previous works.
We present a short analytic proof of the equality between the analytic and combinatorial torsion. We use the same approach as in the proof given by Burghelea, Friedlander and Kappeler, but avoid using the difficult Mayer-Vietoris type…
We present a proof of the Chevalley-Weil Theorem that is somewhat different from the proofs appearing in the literature and with somewhat weaker hypotheses, of purely topological type. We also provide a discussion of the assumptions, and an…
This article presents a clear proof of the Riemann Mapping Theorem via Riemann's method, uncompromised by any appeals to topological intuition.
We present a short and self-contained proof of the choosability version of Brooks' theorem.
We summarize results concerning the Bernstein property of differential equations.
In this note we exhibit a very simple proof of McNaughton Theorem, almost right out of the definitions, and at the same time we observe that this theorem does not depend of Chang's completeness theorem.
In the case of monotone independence, the transparent understanding of the mechanism to validate the central limit theorem (CLT) has been lacking, in sharp contrast to commutative, free and Boolean cases. We have succeeded in clarifying it…
This expository note gives a digest version of Hormander's propagation of singularities theorem for the wave equation.
We give an infinite number of proofs of Pythagoras theorem.Some can be classified as `self-similar proofs'.
We find an elementary proof for Voiculescu's theorem on the polar decomposition of circular variables.
We show the integrality of the simple Hurwitz numbers. The main tool is the cut-and-join operator, and our proof is a purely combinatorial one.
We provide a proof of a variant of the Landau-Siegel Zeros conjecture.
We give a combinatorial upper bound for the gonality of a curve that is defined by a bivariate Laurent polynomial with given Newton polygon. We conjecture that this bound is generically attained, and provide proofs in a considerable number…
We give a short and self-contained proof of a theorem of Ledermann and Neumann stating that there are only finitely many finite groups with a given number of automorphisms. We also discuss the history of related conjectures.
We prove a uniformization theorem in complex algebraic geometry.
In this paper, we provide an easy proof of the Four-colour Theorem in a special case indeed.
We give an elementary and constructive proof for a theorem of de Smit et Lenstra. Note: In version 1, was missing the proof that "completely secant" implies "1-secant"
We prove a result on lower bounds in large dimensions.
We present a much simplified proof of Dehn's theorem on the infinitesimal rigidity of convex polytopes. Our approach is based on the ideas of Trushkina and Schramm.