Related papers: Problems and memories
This note is a continuation of an earlier paper by the authors. We describe improved constructions addressing a question of Erd\H{o}s and Szemer\'edi on sums and products of real numbers along the edges of a graph. We also add a few…
According to Paul Erd\H{o}s [Some notes on Tur\'an's mathematical work, J. Approx. Theory 29 (1980), page 4] it was Paul Tur\'an who "created the area of extremal problems in graph theory". However, without a doubt, Paul Erd\H{o}s…
This is a non-standard paper, containing some problems in set theory I have in various degrees been interested in. Sometimes with a discussion on what I have to say; sometimes, of what makes them interesting to me, sometimes the problems…
One of the themes of this paper is recent results on large gaps between primes. The first of these results has been achieved in the paper [12] by Ford, Green, Konyagin and Tao. It was later improved in the joint paper [13] of these four…
We discuss some aspects of Extrapolation theory. The presentation includes many examples and open problems.
In this survey article we discuss key open problems which could serve as a guidance for further research directions of multiplicative ideal theory and factorization theory.
In connection to the development of the field of Combinatorics on Words, we present a list of open problems and conjectures that were stated during the ten last meetings WORDS. We wish to continually update the present document by adding…
This survey article collects a few of my favorite open problems of Branko Gr\"{u}nbaum.
An attempt of a new kind of complexity anthropology is considered.
I present some reminiscences, both personal and scientific, over a lifetime of admiration of, and friendship with, one of the Grandmasters of our subject.
While I was dealing with a brain injury and finding it difficult to work, two friends (Derek Westen, a friend of the KITP, and Steve Shenker, with whom I was recently collaborating), suggested that a new direction might be good. Steve in…
According to a classical result of Spencer, Szemer\'edi, and Trotter (1984), the maximum number of times the unit distance can occur among $n$ points in the plane is $O(n^{4/3})$. This is far from Erd\H{o}s's lower bound, $n^{1+O(1/\log\log…
The problems and solutions contained here, all associated with nonlinear recurrences and long-term trends, are new (as far as is known).
On the occasion of the 40-th anniversary of IHES I present a few scientific reminiscences: most of my scientific life has been marked by my visits and I run through them concluding with the analysis of a problem that originated during my…
We collect some open problems about minimal presentations of numerical semigroups and, more generally, about defining ideals and free resolutions of their semigroup rings and associated graded rings. We emphasize both long-standing problems…
This paper presents a number of problems about mapping class groups and moduli space. The paper will appear in the book "Problems on Mapping Class Groups and Related Topics", ed. by B. Farb, Proc. Symp. Pure Math. series, Amer. Math. Soc.
In large language model-based agents, memory serves as a critical capability for achieving personalization by storing and utilizing users' information. Although some previous studies have adopted memory to implement user personalization,…
An open problem concerning Riemann sums, posed by O. Furdui, is considered.
Inspired by the Erd\H{o}s' problem in Ramsey theory, we propose a dynamical version of the problem and answer it positively for circle maps.
Whenever one has witnessed some event and then sees it reported in the media, one's reaction is the same: "it was not quite like that". It is in this spirit of a frequent first-hand witness that I write this article. I discuss a few…