Related papers: You Can Enter Cantor's Paradise
These notes are the second half of the contents of the course given by the second author at the Bachelier Seminar (8-15-22 February 2008) at IHP. They also correspond to topics studied by the first author for her Ph.D.thesis.
Generalizing a geometric idea due to J. Sondow, we give a geometric proof for the Cantor's Theorem. Moreover, it is given an irrationality measure for some Cantor series.
These notes are a summary of the problem session discussions at various CANT (Combinatorial and Additive Number Theory Conferences). Currently they include all years from 2009 through 2019 (inclusive); the goal is to supplement this file…
This is an expanded and revised text for a fifteen minute talk given at the University of Queensland Physics Camp, September 2000. The focus is on the goals and motivations for studying quantum information theory, rather than on technical…
These notes are the first half of the contents of the course given by the second author at the Bachelier Seminar (February 8-15-22 2008) at IHP. They also correspond to topics studied by the first author for her Ph.D.thesis.
This is a comment on a collection of statements gathered on the occasion of the Quantum Physics of Nature meeting in Vienna.
The present issue of the series <<Modern Problems in Mathematical Physics>> represents the Proceedings of the Students Training Contest Olympiad in Mathematical and Theoretical Physics and includes the statements and the solutions of the…
This note announces recent exciting progress on the frontier between algebraic topology and probability theory. It is intended for a journal which publishes such announcements (without an abstract, typically in Russian). A description of a…
We introduce and develop a class of \textit{Cantor-winning} sets that share the same amenable properties as the classical winning sets associated to Schmidt's $(\alpha,\beta)$-game: these include maximal Hausdorff dimension, invariance…
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).
In 1994, John Cobb asked: given $N>m>k>0$, does there exist a Cantor set in $\mathbb R^N$ such that each of its projections into $m$-planes is exactly $k$-dimensional? Such sets were described for $(N,m,k)=(2,1,1)$ by L.Antoine (1924) and…
This is a revised version of the notes from the week-long course I gave at the Centre de Recerca Matematica, Barcelona, in September of 2010. The aim is to give a working overview of recent methods and results in "Blaschkean integral…
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…
This article is an expanded version of my talk at the Gathering for Gardner, 2012.
Summary talk at ICHEP 2002, Amsterdam, July 2002. I have kept very close to the content and style of the talk as it was delivered. You may access the associated PowerPoint presentation through a link at…
Despite the huge amount of literature on h-index, few papers have been devoted to the statistical analysis of h-index when a probabilistic distribution is assumed for citation counts. The present contribution relies on showing the available…
This paper summarizes three talks given by the author during a PASI conference in Olinda, Brasil
This text was written to support a Bourbaki seminar given in January 2026 on the subject of the model theory of perfectoid fields, especially on the work of Jahnke and Kartas in their paper "Beyond the Fontaine-Wintenberger theorem", J.…
These are lecture notes written at the University of Zurich during spring 2014 and spring 2015. The first part of the notes gives an introduction to probability theory. It explains the notion of random events and random variables,…
25th anniversary and new building dedication Centre de Recherches Math\'{e}matiques Montr\'{e}al, Canada, October 1994