Related papers: A short proof of Isserlis' theorem
A very short proof of Kneser's theorem via transversal is given.
We give a simple proof of Dorronsoro's theorem and use similar ideas to establish an equivalence for embeddings of vector fields.
A proof is given of Rosenthal's \(\ell_1\) theorem.
In this note we provide a quick proof of the Sklar's Theorem on the existence of copulas by using the generalized inverse functions as in the one dimensional case, but a little more sophisticated.
We introduce the notion of operadic torsors and operadic quasi-torsors. We show that if an operadic (quasi-)torsor between two operads exists, then these operads are (quasi-)isomorphic. As an application we present the (arguably) shortest…
Torelli's theorem is proven by the study of the convolution product of the intersection cohomology sheaf of the thetadivisor.
We prove the so-called Unitary Isotropy Theorem, a result on isotropy of a unitary involution. The analogous previously known results on isotropy of orthogonal and symplectic involutions as well as on hyperbolicity of orthogonal,…
We present a short proof of Szemer\'edi's Theorem using a dynamical system enriched by ideas from model theory. The resulting proof contains features reminiscent of proofs based on both ergodic theory and on hypergraph regularity.
I expound here in a more detailed way a proof of an important Serini's theorem, which I have already sketched in a previous Note. Two related questions are briefly discussed.
This is just a short proof of Kruskal's theorem regarding uniqueness of expressions for tensors, phrased in geometric language.
We give in the present work a new methodology that allows to give isoperimetric proofs, for Kneser's Theorem and Kemperman's structure Theory and most sophisticated results of this type. As an illustration we present a new proof of Kneser's…
We give a new simpler proof of a theorem of Jayne and Rogers.
In this paper we show an index theorem for gerbes
Kolmogorov's invariant torus theorem is proved using a simple fixed point theorem.
In this note, we combine ideas of several previous proofs in order to obtain a quite short proof of Gr\"otzsch theorem.
We give an elementary proof of Kelley's theorem based on a minimax argument. Some applications to related problems are also developed.
We give new proofs of some well-known results from Invariant Theorey using the Kempf-Ness theorem.
We present a proof of Moessner's theorem by double induction, using only basic rules of arithmetic. No prerequisite knowledge is assumed. Familiarity with summation is advised.
In this short exposition we provide a simplified proof of Buser's result for Cheeger's isoperimetric constant.
I present a simple, elementary proof of Morley's theorem, highlighting the naturalness of this theorem.