Related papers: A simple proof of the Lebesgue decomposition theor…

We give an elementary proof of Kelley's theorem based on a minimax argument. Some applications to related problems are also developed.

The paper presents a counterexample to the Hodge conjecture.

In this paper we show an index theorem for gerbes

We give a short proof of Ahlfors' theorem on covering surfaces.

This paper presents a simple proof of Dekel (1986)'s representation theorem for betweenness preferences. The proof is based on the separation theorem.

On compact Riemannian manifolds, we prove a decomposition theorem for arbitrarily bounded energy sequence of solutions of a singular elliptic equation.

We give a simple proof of the increasing strengthening of Arhangel'skii's Theorem. Our proof naturally leads to a refinement of this result of Juh\'asz.

The object of this short note is to prove a theorem and present a conjecture for the number of even entries in the character table of the symmetric group.

We introduce methods that allow to derive continuous-time versions of various discrete-time ergodic theorems. We then illustrate these methods by giving simple proofs and refinements of some known results as well as establishing new results…

We give a geometric proof of the Decomposition Theorem of Beilinson, Bernstein, Deligne and Gabber for the direct image of the intersection cohomology complex under a proper map of complex algebraic varieties. The method rests on new…

We use standard constructions in algebraic geometry and homological algebra to extend the decomposition and hard Lefschetz theorems of T. Mochizuki and C. Sabbah so that they remains valid without the quasi-projectivity assumptions.

The aim of this note, which raises more questions than it answers, is to study natural operations acting on the cohomology of various types of algebras. It contains a lot of very surprising partial results and examples.

In this note I provide two extensions of a particular case of the classical Poncelet theorem.

We give a simple, short and self-contained presentation of Bourgain's discretised projection theorem from 2010, which is a fundamental tool in many recent breakthroughs in geometric measure theory, harmonic analysis, and homogeneous…

We present a short and completely elementary proof for a double sum studied by Brent and Osburn in arXiv:1309.2795v2.

We give a concise proof of the fundamental theorem of smoothing theory in the special case when a smoothing exists.

The aim of this note is to survey the factorizations of the Fibonacci infinite word that make use of the Fibonacci words and other related words, and to show that all these factorizations can be easily derived in sequence starting from…

This is an exposition of Gauss's proof of Descartes's rule of signs.

The main goal of this paper is to give a completely elementary proof for the decomposition theorem of Wright convex functions which was discovered by C.\ T.\ Ng in 1987. In the proof, we do not use transfinite tools, i.e., variants of…

A short and elementary proof is given of a celebrated eigenvalue-perturbation result due to Alfred Brauer.