Related papers: Ernest Borisovich Vinberg
This paper mainly contributes to a classification of statistical Einstein manifolds, namely statistical manifolds at the same time are Einstein manifolds. A statistical manifold is a Riemannian manifold, each of whose points is a…
Reparametrization invariant Sobolev metrics on spaces of regular curves have been shown to be of importance in the field of mathematical shape analysis. For practical applications, one usually discretizes the space of smooth curves and…
This paper has two parts. In the first part we construct arithmetic models of Bost-Connes systems for arbitrary number fields, which has been an open problem since the seminal work of Bost and Connes [3]. In particular our construction…
This article provides a historical overview of Geometry of Numbers. 1. Figures, 2. The circuit problem and its relatives, 3. Minkowski lattice point set, 4. The young Hermann Minkowski, 5. The geometry of numbers develops, 6. Minkowski…
Ya.B. Zeldovich was a pre-eminent Soviet physicist whose seminal contributions spanned many fields ranging from physical chemistry to nuclear and particle physics, and finally astrophysics and cosmology. March 8, 2014 marks Zeldovich's…
Introduction for a special issue of Physica E dedicated to the memory of Markus B\"uttiker.
The mathematical achievements of Harry Kesten since the mid-1950s have revolutionized probability theory as a subject in its own right and in its associations with aspects of algebra, analysis, geometry, and statistical physics. Through his…
With this note, we remember our friend Maria Krawczyk, who passed away this year, on May 24th. We briefly outline some of her physics interests and main accomplishments, and her great human and moral qualities.
This paper is a commentary and a reading guide to three papers by Herbert Busemann, \"Uber die Geometrien, in denen die "Kreise mit unendlichem Radius" die k\"urzesten Linien sind." (On the geometries where circles of infinite radius are…
The Lyubeznik numbers are invariants of a local ring containing a field that capture ring-theoretic properties, but also have numerous connections to geometry and topology. We discuss basic properties of these integer-valued invariants, as…
The process launched by Lobachevsky. The movement of the Kazan school of geometry towards physics. Personal memories of Alexei Zinovievich Petrov, the great Kazan geometer and theoretical physicist, who became the Author's Guiding Star.…
We determine the Batalin-Vilkovisky Lie algebra structure for the integral loop homology of special unitary groups and complex Stiefel manifolds. It is shown to coincide with the Poisson algebra structure associated to a certain odd…
A number of geometric inequalities for convex sets arising from Brunn's concavity principle have recently been shown to yield local stochastic formulations. Comparatively, there has been much less progress towards stochastic forms of…
This article reviews the biography of the Swiss mathematician Marcel Grossmann (1878-1936) and his contributions to the emergence of the general theory of relativity. The first part is his biography, while the second part reviews his…
We give a proof of a conjecture raised by Michael Finkelberg and Andrei Ionov. As a corollary, the coefficients of multivariable version of Kostka functions introduced by Finkelberg and Ionov are non-negative.
G\"unter Hellwig was the author of influential textbooks on PDEs and differential operators of mathematical physics, an enthusiastic and inspiring teacher to generations of engineers, organiser of PDE conferences at Oberwolfach and a…
David Mumford made groundbreaking contributions in many fields, including the pure mathematics of algebraic geometry and the applied mathematics of machine learning and artificial intelligence. His work in both fields influenced my career…
In this paper I shall try to sketch some typical aspects of Erich Lehmann's contributions to statistics through his research, his teaching, his service to the profession and his personality.
This paper, which is dedicated to Alan Turing on the 50th anniversary of his death, gives an overview and discusses the philosophical implications of incompleteness, uncomputability and randomness.
In this note, we sketch an approach to the problems of equivariant birational geometry developed by M. Kontsevich and Yu. Tschinkel, where Burnside invariants were introduced. We are making explicit the role of Nori constructions in this…