Related papers: Notes on symmetric spaces
I discuss several issues related to "classical" spacetime structure. I review Galilean, Newtonian, and Leibnizian spacetimes, and briefly describe more recent developments. The target audience is undergraduates and early graduate students…
This is a survey paper on the space of symplectic structures on closed 4-manifolds, for the Proceedings ICCM 2004
The symmetric subpace has many applications in quantum information theory. This review article begins by explaining key background facts about the symmetric subspace from a quantum information perspective. Then we review, and in some places…
These are lectures notes for the introductory graduate courses on geometric complexity theory (GCT) in the computer science department, the university of Chicago. Part I consists of the lecture notes for the course given by the first author…
We overview main topics and ideas in spaces with their scalar curvatures bounded from below, and present a more detailed exposition of several known and some new geometric constraints on Riemannian spaces implied by the lower bounds on…
We introduce strings in metric spaces and define string complexes of metric spaces. We describe the class of 2-dimensional topological spaces which arise in this way from finite metric spaces.
These Lectures have been given at Laboratori Nazionali di Frascati in the month of March, 2005. The main idea was to provide our young collegues, who joined us in our attempts to understand the structure of $N$-extended supersymmetric…
These are lecture notes of a course taken in Leipzig 2023, spring semester. It deals with extremal combinatorics, algebraic methods and combinatorial geometry. These are not meant to be exhaustive, and do not contain many proofs that were…
We provide a simple proof that conformally semi-symmetric spacetimes are actually semi-symmetric. We also present a complete refined classification of the semi-symmetric spacetimes.
In this paper we generalize a result in [1], showing that an arbitrary Riemannian symmetric space can be realized as a closed submanifold of a covering group of the Lie group defining the symmetric space. Some properties of the subgroups of…
These are lecture notes of a mini-course given by the first author in Moscow in July 2019, taken by the second author and then edited and expanded by the first author. They were also a basis of the lectures given by the first author at the…
These are notes of a series of lectures on sieves, presented during the Special Activity in Analytic Number Theory, at the Max-Planck Institute for Mathematics in Bonn, during the period January--June 2002.
The article surveys published and not yet published results about moduli spaces of algebraic surfaces.
This paper is a continuation of the papers [2,3,4,5,6]. In this paper the osculating spaces of arbitrary order of a manifold embedded in Euclidean space are considered. A better estimation of their dimensions as well as the description of…
In this series of lectures presented at the CIMPA Winter School on Discrete Integrable Systems in Pondicherry, India, in February, 2003 we give a review of the application of Lie point symmetries, and their generalizations to the study of…
The article contains a few questions and speculations related to the moduli spaces of curves, K3 surfaces, maps, and sheaves presented in the problem session of the AGNES conference in Amherst (April 2010).
These are lecture notes of the lecture on elementary celestial mechanics read at Technische Universitaet Dresden, Dresden, Germany from 2000 till 2011.
These notes are a written version of a set of lectures given at TASI-02 on the topic of precision electroweak physics.
These notes are an expanded version of an introductory lecture on contact geometry given at the 2001 Georgia Topology Conference. They are intended to present some of the "topological" aspects of three dimensional contact geometry.
Here we consider a few topics related to Lipschitz classes for functions and curves in metric spaces.