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The hypothesis concerning the off-site continuum existence is investigated from the point of view of the mathematical theory of sets. The principles and methods of the mathematical description of the physical objects from different off-site…

The aim of this note is to show that Poincar\'e inequalities imply corresponding weighted versions in a quite general setting. Fractional Poincar\'e inequalities are considered, too. The proof is short and does not involve covering…

D.R. Woodall's definition of a 'musquash' is extended to that of a 'bi-musquash' and the existence/uniqueness of these is discussed.

Infinity, in various guises, has been invoked recently in order to `explain' a number of important questions regarding observable phenomena in science, and in particular in cosmology. Such explanations are by their nature speculative. Here…

We state the analogs of Kontsevich's formality conjecture for Hochschild and cyclic chains, as well as their

These are the notes (in French) for a Bourbaki talk on the twisted Lang-Weil estimates of Hrushovski, following a recent proof of Shuddhodan and Varshavsky.

The recently published "Oxford Questions" are supplemented with annotations concerning: doctrine of wave packets collapse (and sub- sidiarily Schrodinger's cat thought experiment), description of quan- tum measurements respectively…

The present notes are based on a course on Cherednik algebras given by the first author at MIT in the Fall of 2009. Their goal is to give an introduction to Cherednik algebras, and to review the web of connections between them and other…

The paper contains an alternative proof of M. Kontsevich Formality Theorem.

I discuss the computational methods behind the formulation of some conjectures related to variants on Andrews' $q$-Dyson conjecture.

This paper constructs a Riemann surface associated to the icosahedron and discusses the geodesics associated to a flat metric on this surface. Because of the icosahedral symmetry, this is a distinguished special case of the example treated…

It was conjectured that multiplicity of a singularity is bi-Lipschitz invariant. We disprove this conjecture, constructing examples of bi-Lipschitz equivalent complex algebraic singularities with different values of multiplicity.

We present a history of the Baum-Connes conjecture, the methods involved, the current status, and the mathematics it generated.

We summarise some aspects of experiments currently being built or planned, and indulge in wild speculation about possibilities on the more distant horizon.

This is a summary of the theoretical contributions to the QCD session of the 47th Rencontre de Moriond, including some perspectives on the implications of the reported experimental results on the status of our theoretical understanding.

I summarise the theoretical talks at Moriond 2015, with emphasis on naturalness.

These are the lecture notes from a five-hour mini-course given at the Winter School on Galois Theory held at the University of Luxembourg in February 2012. Their aim is to give an overview of Serre's modularity conjecture and of its proof…

We survey recent developments on the Restriction conjecture.

Brief lecture notes for a course about random matrices given at the University of Cambridge.

This is a comment on a collection of statements gathered on the occasion of the Quantum Physics of Nature meeting in Vienna.