Related papers: A variation on the homological nerve theorem

A proof of Sendov's conjecture is given.

We present simple and direct proof to an important case of Nash-Moser-Ekeland theorem.

A new equivalence notion between non-stationary subdivision schemes, termed asymptotical similarity, which is weaker than asymptotical equivalence, is introduced and studied. It is known that asymptotical equivalence between a…

Using algebraic transformations and equivalent reformulations we derive a number of new results from some earlier ones (by the author) in more accepted terms closely related to well-known conjectures of Bondy and Jung including a number of…

We present new, unified proofs for the cell-like, $\mathbb{Z}/p$-, and $\mathbb{Q}$-resolution theorems. Our arguments employ extensions that are much simpler then those used by our predecessors. The techniques allow us to solve problems…

A proof is given of Rosenthal's \(\ell_1\) theorem.

We prove a better coloring theorem for aleph_4 and even aleph_3. This has a general topology consequence.

A new generalization of the classical separate algebraicity theorem is suggested and proved.

We prove some extensions of Andrews inequality.

Kolmogorov's invariant torus theorem is proved using a simple fixed point theorem.

We give an alternative proof of Madsen-Weiss' generalized Mumford conjecture. Our proof is based on ideas similar to Madsen-Weiss' original proof, but it is more geometrical and less homotopy theoretical in nature. At the heart of the…

We show that the classification diagram of a relative $\infty$-category arising from a relative simplicial category is equivalent to the levelwise nerve. Applications include the comparison of the diagonal of the levelwise nerve and the…

We claim to resolve the P=?NP problem via a formal argument for P=NP.

In this article using elementary school level Geometry we observe an alternative proof of Pythagorean Theorem from Heron's Formula.

New cases of the multiplicity conjecture are considered.

In this note we prove a weighted version of the Khintchine inequalities.

We give a new proof of Bogomolov's instability theorem. Furthermore we prove that it is equivalent to a statement which characterizes when the first cohomology group of a suitable divisor does not vanish.

We survey the classical results of the Dirichlet Approximation Theorem.

We prove a stability theorem for the elliptic Harnack inequality: if two weighted graphs are equivalent, then the elliptic Harnack inequality holds for harmonic functions with respect to one of the graphs if and only if it holds for…

The purpose of this note is to rephrase Speyer's elegant topological proof for Kasteleyn's Theorem in a simple graph theoretical manner.