Related papers: One recent development of the M_3 vs. M_1 problem
The first section of this modest survey reviews some basic notions and describes some families of examples, and the second section briefly indicates some general aspects of analysis on metric spaces. The remaining three sections are…
This essay considers ways that recent uses of computers in mathematics challenge contemporary views on the nature of mathematical understanding. It also puts these challenges in a historical perspective and offers speculation as to a…
This is a survey of recent advances in commutative algebra, especially in mixed characteristic, obtained by using the theory of perfectoid spaces. An explanation of these techniques and a short account of the author's proof of the direct…
Current problems in particle physics are reviewed from the viewpoint of theories possessing extra spatial dimensions.
We study K3 surfaces over non-closed fields and relate the notion of derived equivalence to arithmetic problems.
A new class of 3-manifold invariants is constructed from representations of the category of framed tangles.
We survey the history as well as recent progress in the Yang problem concerning the existence of complete bounded complex submanifolds of the complex Euclidean spaces. We also point out some open questions on the topic.
In this paper we consider the $X_s$ spaces that lie between $H^1(R^n)$ and $L^1(R^n)$. We discuss the interpolation properties of these spaces, and the behavior of maximal functions and singular integrals acting on them.
In the paper Description of the $K$-spaces by means of $J$-spaces and the reverse problem, Math. Nachr. 296 (2023), no. 9, 4002--4031, we have establish conditions under which the limiting $K$-space $(X_0,X_1)_{0,q,b;K}$, involving a slowly…
The question in the title is discussed briefly, with emphasis on a few basic examples and their properties.
We study the interrelation of space functions of groups and the space complexity of the algorithmic word problem in groups.
This paper is based on my talk at ICM on recent progress in a number of classical problems of linear algebra and representation theory, based on new approach, originated from geometry of stable bundles and geometric invariant theory.
We survey some recent developments on various notions of semipositivity for (1,1)-classes on complex manifolds, and discuss a number of open questions.
The possible spatial transformation properties of tetrons are discussed.
The moduli space of degree $d$ morphisms on $\mathbb{P}^1$ has received much study. McMullen showed that, except for certain families of Latt\`es maps, there is a finite-to-one correspondence (over $\mathbb{C}$) between classes of morphisms…
This note tries to give an answer to the following question: Is there a sufficiently rich class of metric vector spaces such that sufficiently large spaces of continuous linear maps between them are metrizable?
We prove the double bubble conjecture in the three-sphere $S^3$ and hyperbolic three-space $H^3$ in the cases where we can apply Hutchings theory: 1) in $S^3$, each enclosed volume and the complement occupy at least 10% of the volume of…
We utilize the close relation between the complex space $\textbf{C}^2$ and the real space $\textbf{R}^3$ to reformulate quantum mechanics in a manner which allows to, either or both, describe magnetic monopoles and quantize the underlying…
It is well known that knots are countable in ordinary knot theory. Recently, knots {\it with intersections} have raised a certain interest, and have been found to have physical applications. We point out that such knots --equivalence…
The corrections to the gravitational potential due to a Sol extra dimensional compact manifold, denoted as $M_A^3$, are studied. The total spacetime is of the form $M^4\times M_A^3$. The range of the Sol corrections is investigated and…