Related papers: The work of Andrei Okounkov

This is expanded text of a lecture delivered by the author at the conference "Mat\'eriaux pour l'Histoire des Math\'ematiques au XX\`eme si\`ecle", which took place in Nice in January 1996. The task was to describe one area in the…

The review presents rigorous results of the theory of fundamental equations of evolution of many-particle systems with collisions and also considers their connection with nonlinear kinetic equations describing the collective behavior of…

In the "6D treatment of Special Relativity" proposed by Igor A. Urusovskii one deals with universal light-like motion of matter pre-elements in the extended (3+3) space and with their regular rotation in the additional 3-space. On the other…

This is a mainly expository article honoring my recently deceased friend and collaborator Krzysztof Galicki who died after a tragic hiking accident. I give a review of our recent work in Sasakian geometry. A few new results are also…

We develop a theory for the representation of opaque solids as volumes. Starting from a stochastic representation of opaque solids as random indicator functions, we prove the conditions under which such solids can be modeled using…

This is a brief introduction to the theory of Enriques surfaces over arbitrary algebraically closed fields. Some new results about automorphism groups of Enriques surfaces are also included.

The Fields Medal, often referred as the Nobel Prize of mathematics, is awarded to no more than four mathematician under the age of 40, every four years. In recent years, its conferral has come under scrutiny of math historians, for…

The present article proposes a review of the most recent results obtained in the study of Novikov's problem on the description of the geometry of the level lines of quasi-periodic functions in the plane. Most of the paper is devoted to the…

The purpose of this book is to build up the fundament of an Arakelov theory over adelic curves in order to provide a unified framework for the researches of arithmetic geometry in several directions.

This chapter surveys the advances of the past decade arising from the contributions of Indian mathematicians in the broad areas of operator algebras and operator theory. It brings together the work of twenty mathematicians and their…

This is a write-up of some lectures I gave in the Fall of 2021 at the Fields Institute in Toronto, as part of the Thematic Programme on Trends in Pure and Applied Model Theory. The goal of the module was to give a quick introduction to the…

Review of the two volume set "The Quantum Theory of Fields" by S. Weinberg is presented.

In this exposition of the equality and inequality of Minkowski for multiplicity of ideals, we provide simple algebraic and geometric proofs. Connections with mixed multiplicities of ideals are explained.

In this paper, we establish an exponential inequality for random fields, which is applied in the context of convergence rates in the law of large numbers and H\"olderian weak invariance principle.

This article presents a neural network approach for estimating the covariance function of spatial Gaussian random fields defined in a portion of the Euclidean plane. Our proposal builds upon recent contributions, expanding from the purely…

Talk presented at the conference ``Historical and Philosophical Reflections on the Foundations of Quantum Field Theory,'' at Boston University, March 1996. It will be published in the proceedings of this conference.

I present a brief review on some of the recent developments in topological quantum field theory. These include topological string theory, topological Yang-Mills theory and Chern-Simons gauge theory. It is emphasized how the application of…

We survey a decade worth of work pertaining to the nodal structures of random fields, with emphasis on the transformative techniques that shaped the field.

This is an enhanced version of the author's 1998 Harvard Ph.D. thesis, as published by IMRN in 2005. We propose an extension of Bogomolov's conjecture about commutator subgroups of Galois groups to arbitrary fields. A somewhat weaker…

In this exposition we discuss the theory of algebraic extensions of valued fields. Our approach is mostly through Galois theory. Most of the results are well-known, but some are new. No previous knowledge on the theory of valuations is…