相关论文: Georg Cantor and his heritage
Life and the mathematical legacy of the great mathematician A.V. Pogorelov.
We continue the investigation of Gregory trees and the Cantor Tree Property carried out by Hart and Kunen. We produce models of MA with the Continuum arbitrarily large in which there are Gregory trees, and in which there are no Gregory…
This is an expository paper detailing some of the recent advances on the problem, with emphasis on the number-theoretic method developed in my paper with Bond and Volberg for rational product sets (arXiv:1109.1031).
We present a point of view on results of the paper of Geronimo and Johnson [Comm. Math, Phys. 193 (1998)] that allow infinitely dimensional generalization up to the case when spectrum is supported on a Cantor set of positive Lebesgue…
Using an iterative tree construction we show that for simple computable subsets of the Cantor space Hausdorff, constructive and computable dimensions might be incomputable.
The world of mathematics is often considered abstract, with its symbols, concepts, and topics appearing unrelated to physical objects. However, it is important to recognize that the development of mathematics is fundamentally influenced by…
We study the topology and the Hausdorff dimension of a random Cantor set with overlaps, generated by an iterated function system with scaling ratio equal to the Golden Mean. The results extend known formulas to a case where the Open Set…
We review various combinatorial problems with underlying classical or quantum integrable structures. (Plenary talk given at the International Congress of Mathematical Physics, Aalborg, Denmark, August 10, 2012.)
We discuss the legacy of Alan Turing and his impact on computability and analysis.
This is an exposition of the contributions of L\'aszl\'o Lov\'asz to mathematics and computer science written on the occasion of the bestowal of the Abel Prize~2021 to him. Our survey, of course, cannot be exhaustive. We sketch remarkable…
This survey synthesizes the principal descriptive set-theoretic perspectives on deterministic Cantor sets on the real line and charts directions for future study. After recounting their historical genesis and compiling an up-to-date…
Discussion of ``The Dantzig selector: Statistical estimation when $p$ is much larger than $n$'' by Emmanuel Candes and Terence Tao [math/0506081]
The main scientific heritage of Corrado B\"ohm consists of ideas about computing, concerning concrete algorithms, as well as models of computability. The following will be presented. 1. A compiler that can compile itself. 2. Structured…
I was interested in the work of Solomon Marcus in Mathematical Linguistics as a high-school student. Later, I had the opportunity to discuss with him about many topics. He was a polymath. We wrote a paper together, and I refereed an…
These are reminiscences of I.M.Gelfand's mathematical seminar of 1970s-1980s. The essay will appear in the March 2016 issue of Notices of the AMS.
We are grateful to all discussants of our re-visitation for their strong support in our enterprise and for their overall agreement with our perspective. Further discussions with them and other leading statisticians showed that the legacy of…
We investigate some relations between number theory and spectral measures related to the harmonic analysis of a Cantor set. Specifically, we explore ways to determine when an odd natural number $m$ generates a complete or incomplete Fourier…
This survey contains a recollection of results, problems and conversations which go back to the early years of Representation Theory and Tilting Theory.
We establish formulas for bounds on the Haudorff measure of the intersection of certain Cantor sets with their translates. As a consequence we obtain a formula for the Hausdorff dimensions of these intersections.
This article surveys the known results (and not very well-known results) associated with Cantor's pairing function and the Rosenberg-Strong pairing function, including their inverses, their generalizations to higher dimensions, and a…