Related papers: The work of Andrei Okounkov
A study of the intersection theory on the moduli space of Riemann surfaces with boundary was recently initiated in a work of R. Pandharipande, J. P. Solomon and the third author, where they introduced open intersection numbers in genus 0.…
In recent years, random matrices have come to play a major role in computational mathematics, but most of the classical areas of random matrix theory remain the province of experts. Over the last decade, with the advent of matrix…
This article is dedicated to the centenary of the birth of Aleksandr D. Alexandrov (1912-1999). His functional-analytical approach to the solving of the Minkowski problem is examined and applied to the extremal problems of isoperimetric…
Based on the work of Hahn, Baer, Ostrowski, Krull, Kaplansky and the Artin-Schreier theory, and stimulated by a paper of S. Lang in 1953, the theory of real places and convex valuations has witnessed a remarkable development and has become…
Oleg D. Jefimenko's electrodynamics textbook is unique in its approaches to deriving the electric and magnetic fields of arbitrary charge and current distributions and of an arbitrarily moving point charge. However, an uncommon form of the…
A concise survey of the contribution of D.I. Blokhintsev to the quantum physics, including solid state physics, physics of metals, surface physics, statistical physics and optics is given. These achievements have been considered in the…
The works prsented in this habilitation thesis can be gathered in six themes. Works on the implicit function theorem and the geometry of numerical schemes. On the existence of an exponential map on an infinite dimensioal Lie group. Holonomy…
This paper gives a brief overview of some new work in number theory and algebra, and also studies the arithmetic and algebraic properties of Minkowski balls and spheres. The content of the paper is presented in more detail in the table of…
This paper, which is a summary (in which considerable creative license has been taken) of the author's talk at the sixth international conference on $p$-adic mathematical physics and its applications (CINVESTAV, Mexico City, October 2017),…
This is a survey paper with some original results of the author on refined versions of the Azuma-Hoeffding inequality with some examples that are related to information theory. This work has evolved to the joint paper with Maxim Raginsky in…
We give a proposal for future development of the model theory of valued fields. We also summarize some recent results on p-adic numbers.
In the years from 2001 to 2006, Guseinov and his coworkers published 40 articles on the derivation and application of one-range addition theorems. In E. J. Weniger, Extended Comment on ``One-Range Addition Theorems for Coulomb Interaction…
This short paper being devoted to some aspects of the inverse problem of the representation theory treats several themes, which have their origins in the researches of F.A.Berezin, D.P.Zhelobenko, V.P.Maslov and his group, in context of the…
This expository paper is based on the lectures given at the program `Modular Representation Theory of Finite and $p$-adic Groups' at the National University of Singapore. We are concerned with recent results on representation theory and…
We present the summary of the general discussion on the probabilistic foundations of quantum theory that took place during the round table at the Int. Conf. "Foundations of Probability and Physics", V\"axj\"o, Sweden-2000. It is possible to…
Written for the book "Mathematicians from Saint Petersburg and their theorems".
Many complex systems are characterized by intriguing spatio-temporal structures. Their mathematical description relies on the analysis of appropriate correlation functions. Functional integral techniques provide a unifying formalism that…
We examine situations, where representations of a finite-dimensional $F$-algebra $A$ defined over a separable extension field $K/F$, have a unique minimal field of definition. Here the base field $F$ is assumed to be a $C_1$-field. In…
I comment on some theoretical work presented at QCD Moriond 2006.
We discuss our work on pointwise inequalities for the gradient which are connected with the isoperimetric profile associated to a given geometry. We show how they can be used to unify certain aspects of the theory of Sobolev inequalities.…