Related papers: On the Choi-Effros multiplication

We provide a short proof of the 1-dimensional flat chain conjecture.

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

In this note, we present a probabilistic proof of the well-known finite geometric series. The proof follows by taking the moments of the sum and the difference of two independent exponentially distributed random variables.

Simple constructions are given for finite semifields that include as special cases both old semifields and recently constructed semifields.

We generalize Bourgain's discretized projection theorem to higher rank situations. Like Bourgain's theorem, our result yields an estimate for the Hausdorff dimension of the exceptional sets in projection theorems formulated in terms of…

An introduction is given to the logic of sheaves of structures and to set theoretic forcing constructions based on this logic. Using these tools, it is presented an alternative proof of the independence of the Continuum Hypothesis; which…

We give an elementary, Fourier-free proof of Roth's theorem. The proof follows Roth's original density-increment strategy, but replaces the usual Fourier-analytic step with a direct combinatorial argument involving averages over…

We define E-theory for separable C*-algebras over second countable topological spaces and establish its basic properties. This includes an approximation theorem that relates the E-theory over a general space to the E-theories over finite…

We show how to translate the task of computing the multiplicative structure of a Chow ring of a projective homogeneous variety into an easily understandable combinatorial task of calculating in the corresponding polynomial ring. The…

We add another brick to the large building comprising proofs of Pick's theorem. Although our proof is not the most elementary, it is short and reveals a connection between Pick's theorem and the pointwise convergence of multiple Fourier…

We present a proof of Roth's theorem that follows a slightly different structure to the usual proofs, in that there is not much iteration. Although our proof works using a type of density increment argument (which is typical of most proofs…

The goal of this paper is to define a certain Chow weight structure for the category of Voevodsky's motivic complexes with integral coefficients (as described by Cisinski and Deglise) over any excellent finite-dimensional separated scheme…

We obtain examples of smooth projective varieties over $\mathbb{C}$ that violate the integral Hodge conjecture and for which the total Chow group is of finite rank. Moreover, we show that there exist such examples defined over number…

We prove an analogue of the Prime Number Theorem for short intervals on a smooth projective geometrically irreducible curve of arbitrary genus over a finite field. A short interval "of size E" in this setting is any additive translate of…

We present a short and self-contained proof of the choosability version of Brooks' theorem.

We prove a Wong-Rosay type theorem for a domain with a piecewise smooth generic strictly pseudoconvex boundary point.

We prove that every quasi-projective semi log canonical pair has a quasi-log structure with several good properties. It implies that various vanishing theorems, torsion-free theorem, and the cone and contraction theorem hold for semi log…

Using Easton collapses, we give a simplified construction of a model in which Chang's Conjecture for triples holds.

A new transparent proof of the well known good compactification theorem for the complex torus $(\Bbb C^*)^n$ is presented. This theorem provides a powerful tool in enumerative geometry for subvarieties in the complex torus. The paper also…

We generalise the Caristi Fixed Point Theorem to the mappings of the complete semi-metric spaces.