Related papers: Some open problems and conjectures on submanifolds…

First the title could be also understood as ``3-manifolds related by non-zero degree maps" or "Degrees of maps between 3-manifolds" for some aspects in this survey talk. The topology of surfaces was completely understood at the end of 19th…

In what follows we give a quick tour through the field of minimal submanifolds, starting at the definition and the classical results and ending up with current areas of research.

Following my plenary lecture on ICMP2000 I review my results concerning two closely related topics: topological quantum field theories and the problem of quantization of gauge theories. I start with old results (first examples of…

An overview of quantum computing and in particular the Hidden Subgroup Problem are presented from a mathematical viewpoint. Detailed proofs are supplied for many important results from the literature, and notation is unified, making it…

This note is based on a lecture delivered by the author at the Second Conference on Differential Geometry, held in Fez in October 2024. It offers an accessible introduction to biharmonic and biconservative submanifolds, exploring the…

This work is motivated by two problems: 1) The approach of manifolds and spaces by triangulations. 2) The complexity growth in sequences of polyhedra. Considering both problems as related, new criteria and methods for approximating smooth…

This is a survey article on finite type invariants of 3-manifolds written for the Encyclopedia of Mathematical Physics to be published by Elsevier.

The class of the hypercomplex pseudo-Hermitian manifolds is considered. The flatness of the considered manifolds with the 3 parallel complex structures is proved. Conformal transformations of the metrics are introduced. The conformal…

Finite metric spaces arise in many different contexts. Enormous bodies of data, scientific, commercial and others can often be viewed as large metric spaces. It turns out that the metric of graphs reveals a lot of interesting information.…

The article covers developments in the representation theory of finite group schemes over the last fifteen years. We start with the finite generation of cohomology of a finite group scheme and proceed to discuss various consequences and…

A submanifold $M$ of a Euclidean $m$-space is said to be biharmonic if $\Delta \overrightarrow H=0$ holds identically, where $\overrightarrow H$ is the mean curvature vector field and $\Delta$ is the Laplacian on $M$. In 1991, the author…

Cubic complexes appear in the theory of finite type invariants so often that one can ascribe them to basic notions of the theory. In this paper we begin the exposition of finite type invariants from the `cubic' point of view. Finite type…

We develop the theory of Diophantine approximation for systems of simultaneously small linear forms, which coefficients are drawn from any given analytic non-degenerate manifolds. This setup originates from a problem of Sprind\v{z}uk from…

A mostly expository account of old questions about the relationship between polyhedra and topological manifolds. Topics are old topological results, new gauge theory results (with speculations about next directions), and history of the…

This survey/expository article covers a variety of topics related to the "topology at infinity" of noncompact manifolds and complexes. In manifold topology and geometric group theory, the most important noncompact spaces are often…

We discuss recent progress many problems in random matrix theory of a combinatorial nature, including several breakthroughs that solve long standing famous conjectures.

Associated to any supermanifold is a filtration by spaces, referred to as thickenings. It is the objective of this article to study them up to a certain equivalence and then up to isomorphism in the complex-analytic setting. We study them…

This paper can be considered as an extension to our paper [On symplectically harmonic forms on six-dimensional nilmanifolds, Comment. Math. Helv. 76 (2001), n 1, 89-109]. Also, it contains a brief survey of recent results on symplectically…

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.

For a certain class of compact oriented 3-manifolds, M. Goussarov and K. Habiro have conjectured that the information carried by finite-type invariants should be characterized in terms of ``cut-and-paste'' operations defined by the lower…