Related papers: Coarse geometry

The nonlinear geometry of operator spaces has recently started to be investigated. Many notions of nonlinear embeddability have been introduced so far, but, as noticed before by other authors, it was not clear whether they could be…

We consider asymptotic dimension of coarse spaces. We analyse coarse structures induced by metrisable compactifications. We calculate asymptotic dimension of coarse cell complexes. We calculate the asymptotic dimension of certain negatively…

This is a survey talk on the study of Gel'fand-Dorfman bialgebras.

This article is a survey of results involving conformal deformation of Riemannian metrics and fully nonlinear equations.

This article uses homological methods for evaluating compactly supported cohomology groups of noncompact toric surfaces

Using geometric homology and cohomology we give a simple and conceptual proof of the Thom isomorphism theorem.

This is a survey on the Fano schemes of linear spaces, conics, rational curves, and curves of higher genera in smooth projective hypersurfaces, complete intersections, Fano threefolds, etc.

I give a short review of the theory of twisted symmetries of differential equations, emphasizing geometrical aspects. Some open problems are also mentioned.

This is a survey paper of the developments on the geometric Bogomolov conjecture. We explain the recent results by the author as well as previous works concerning the conjecture. This paper also includes an introduction to the height theory…

We show that topological phases include disordered materials if the underlying invariant is interpreted as originating from coarse geometry. This coarse geometric framework, grounded in physical principles, offers a natural setting for the…

We survey some topics in ${\mathbb A}^1$-homotopy theory. Our main goal is to highlight the interplay between ${\mathbb A}^1$-homotopy theory and affine algebraic geometry, focusing on the varieties that are "contractible" from various…

These notes are designed for those who either plan to work in differential geometry, or at least want to have a good reason not to do it. We discuss smooth curves and surfaces -- the main gate to differential geometry. We focus on the…

John Roe \cite{Roe lectures} introduced coarse structures for arbitrary sets $X$ by considering subsets of $X\times X$. That definition, while natural for analysts, is a bit more difficult to digest for topologists and geometers. In this…

This work is a continuation of [1]. As in the previous article, here we will describe some interesting ideas and a lot of new theorems in plane geometry related to them.

This is a survey of some recent developments concerning the p-adic cohomology of algebraic varieties over fields of positive characteristic and local fields of mixed characteristic, plus some related areas like p-adic Hodge theory.

This short survey article reviews current understand- ing of the structure of noetherian Hopf algebras. The focus is on homological properties. A number of open problems are listed.

Homology with values in a connection with possibly irregular singular points on an algebraic curve is defined, generalizing homology with values in the underlying local system for a connection with regular singular points. Integration…

This survey paper aims at providing a "literary" anthology of mathematical morphology on graphs. It describes in the English language many ideas stemming from a large number of different papers, hence providing a unified view of an active…

In this short survey we report on the theory of biharmonic maps between Riemannian manifolds.

A new type of sectional curvature is introduced. The notion is purely algebraic and can be located in linear algebra as well as in differential geometry.