Related papers: Dennis Sullivan: Mathematics and physics; manifold…

This article is an overview of some of the remarkable progress that has been made in Sasaki-Einstein geometry over the last decade, which includes a number of new methods of constructing Sasaki-Einstein manifolds and obstructions.

Many distinct problems give birth to Darboux-Halphen system of differential equations and here we review some of them. The first is the classical problem presented by Darboux and later solved by Halphen concerning finding infinite number of…

This is a review of the main physical ideas and examples of applicability in astrophysics and pure physics of a semiclassical theory of dense matter proposed by Pavle Savic and Radivoje Kasanin in the early sixties. A hypothesis, advanced…

We dedicate this to the life and work of Robin Hudson -- a mathematical physicist who developed the peerless quantum stochastic calculus, but who also inspired generations of researchers with both his intellect and wit.

I provide some comments on Arithmetic Teichmuller Spaces constructed in my paper arXiv:2106.11452.

This work is a continuation of the recent study by the authors on approximation theory over the sphere and the ball. The main results define new Sobolev spaces on these domains and study polynomial approximations for functions in these…

Relationships between moduli spaces of curves and sheaves on 3-folds are presented starting with the Gromov-Witten/Donaldson-Thomas correspondence proposed more than 20 years ago with D. Maulik, N. Nekrasov, and A. Okounkov. The descendent…

We present a research mathematician's perspective on current developments around in K-12 mathematics. We share activities, and highlight the different ways in which students' reasoning can progress, such as amount of abstraction,…

This is a non-technical survey of a recent theory of valuations on manifolds constructed in math.MG/0503397, math.MG/0503399, math.MG/0509512, math.MG/0511171 and actually a guide to this series of articles. We review also some recent…

The work consists of solutions of metric problems for convex and finite subsets of geodesic spaces.

This article was written on the occasion of Hans Grauert receiving the Cantor Medallion of the Deutsche Mathematische Vereinigung. It is a brief overview of his mathematical contributions and attempts to convey the author's great respect…

We give a quick tour through many of the classical results in the field of minimal submanifolds, starting at the definition. The field of minimal submanifolds remains extremely active and has very recently seen major developments that have…

A short introduction to the mathematical methods and technics of differential algebras and modules adapted to the problems of mathematical and theoretical physics is presented.

Specification of the strongest possible Bell inequalities for arbitrarily complicated physical scenarios -- any number of observers choosing between any number of observables with any number of possible outcomes -- is currently an open…

1. Translated by Thomas E. Cecil, Department of Mathematics and Computer Science, College of the Holy Cross, Worcester, MA 01610, USA; E-mail address: [email protected] 2. Typed by Wenjiao Yan, School of Mathematical Sciences,…

We review selected achievements of the late Bogdan Mielnik in the field of theoretical physics, with an emphasis on his attempts to go beyond quantum mechanics. Some of his original views on the problems of contemporary society and…

This work aims to define the concept of manifold, which has a very important place in the topology, on digital images. So, a general perspective is provided for two and three-dimensional imaging studies on digital curves and digital…

Beyond normal surfaces there are several open questions concerning 2- dimensional spaces. We present some results and conjectures along this line.

Abelian duality on the closed three-dimensional Riemannian manifold M is discussed. Partition functions for the ordinary U(1) gauge theory and a circle-valued scalar field theory on M are explicitly calculated and compared. It is shown that…

Series of short contributions that are part of Nobel Symposium 162 - Microfluidics arXiv:1712.08369.