Related papers: Speyer's elegant topological proof for Kasteleyn's…

In this short note, we revisit Zeilberger's proof of the classical matrix-tree theorem and give a unified concise proof of variants of this theorem, some known and some new.

We discuss topological versions of the closed graph theorem, where continuity is inferred from near continuity in tandem with suitable conditions on source or target spaces. We seek internal characterizations of spaces satisfying a closed…

Proofs that a smooth morphism is flat available in the literature are long and difficult. We give a short proof of this fact.

We provide a simple proof of Kamp's theorem.

The purpose of this short note is to present a simplified proof of Serre's modularity conjecture using the strong modularity lifting results currently available. This second version includes extra details on definitions and proofs than the…

The purpose of this note is to give an (esentially optimal) effective version of Matsusaka's Big theorem for smooth projective surfaces.

We present a streamlined and simplified proof of the Kakeya set conjecture in $\mathbb{R}^3$.

We develop a family of simple rank one theories built over quite arbitrary sequences of finite hypergraphs. (This extends an idea from the recent proof that Keisler's order has continuum many classes, however, the construction does not…

We give a stack-theoretic proof for some results on families of hyperelliptic curves.

We give a new simpler proof of a theorem of Jayne and Rogers.

A theory graph is a network of axiomatic theories connected with meaning-preserving mappings called theory morphisms. Theory graphs are well suited for organizing large bodies of mathematical knowledge. Traditional and formal proofs do not…

A proof of Sharkovsky's Theorem is given. It is shown how this proof naturally generalizes to looking at maps on graphs and to Sharkovsky-type theorems for these maps. The paper is written at an elementary level and is meant as an…

In this paper we give a new proof of Riemann's well known mapping theorem. The suggested method permits to prove an analog of that theorem for the three dimensional case.

In this paper, we present a short proof of Halin's grid theorem.

The goal of this paper is to formalize the notion of The Compositional Integral in The Complex Plane. We prove a convergence theorem guaranteeing its existence. We prove an analogue of Cauchy's Integral Theorem--and suggest an approach at…

A very short proof of Kneser's theorem via transversal is given.

We prove a spectral decomposition theorem for a well-known self-similar graph, for some finite graphs which are quotients of this graph and for a compactification of it.

We give a short, topological proof that all graphs admit tree-decompositions displaying their topological ends.

In this short note we prove the Borel conjecture for a family of aspherical manifolds that includes higher graph manifolds.

We give a short proof of a theorem of J.-E. Pin (theorem 1.1 below), which can be found in his thesis. The part of the proof which is my own (not Pin's) is a complete replacement of the same part in an earlier version of this paper.