Related papers: Problems and memories
Starting with the unsolved "D\"urer's problem" of edge-unfolding a convex polyhedron to a net, we specialize and generalize (a) the types of cuts permitted, and (b) the polyhedra shapes, to highlight both advances established and which…
We discuss several open problems on spectrally bounded operators, some new, some old, adding in a few new insights.
By using random multilinear maps, we provide new lower bounds for the Erd\H{o}s box problem, the problem of estimating the extremal number of the complete $d$-partite $d$-uniform hypergraph with two vertices in each part, thereby improving…
This article covers my second talk at the Gathering for Gardner in March, 2010. It is about an Odd One Out puzzle I invented, after having been inspired by Martin Gardner. I do not like Odd One Out questions; that is why I invented one.
This note outlines the realizable extension problem for weighted graphs and provides results of a detailed analysis of this problem for the weighted graph $(K_{3,3},l)$. This analysis is then utilized to provide a result relating to the…
One of the great pleasures of working with Imre Leader is to experience his infectious delight on encountering a compelling combinatorial problem. This collection of open problems in combinatorics has been put together by a subset of his…
This note is the written version of conversations with young colleagues on unofficial history, general ideas, unexpected facts and open problems concerning tilting theory.
Presents a history of the evolution of the author's ideas on program-size complexity and its applications to metamathematics over the course of more than four decades. Includes suggestions for further work.
The Halting Problem is a version of the Liar's Paradox.
These informal notes deal with some topics related to analysis on metric spaces.
Leonhard Euler was working for the St. Petersburg Academy of Sciences (Russia) and Prussian Academy of Sciences during various periods of his life. It is not a popular knowledge about Euler's contacts with Polish scientists of his era and…
Despite the several successes of deep learning systems, there are concerns about their limitations, discussed most recently by Gary Marcus. This paper discusses Marcus's concerns and some others, together with solutions to several of these…
We survey the history and recent developments around two decades-old problems that continue to attract a great deal of interest: the slicing $\times 2$, $\times 3$ conjecture of H. Furstenberg in ergodic theory, and the distance set problem…
The neural basis of human memory is incredibly complex. We argue that the diversity of neural systems underlying various forms of memory suggests that any discussion of enhancing 'memory' per se is too broad, thus obfuscating the…
We study the following variant of the Erd\H{o}s distance problem. Given $E$ and $F$ a point sets in $\mathbb{R}^d$ and $p = (p_1, \ldots, p_q)$ with $p_1+ \cdots + p_q = d$ is an increasing partition of $d$ define $$ B_p(E,F)=\{(|x_1-y_1|,…
Seventy-nine physical problems are listed and explained with whose proposed solutions I do not agree. Such disagreements -- even though some of them may simply reflect our preliminary insight into the laws of nature -- have occasionally…
Recent work on Bohr's reply to EPR has helped improve our understanding of Bohr's reply, but further work is needed. In this paper I do two things towards that end. First, I make some elementary points about EPR's argument, which help to…
Making neural networks remember over the long term has been a longstanding issue. Although several external memory techniques have been introduced, most focus on retaining recent information in the short term. Regardless of its importance,…
We present some open problems and describe briefly some possible research directions in the emerging theory of Hardy spaces of Dirichlet series and their intimate counterparts, Hardy spaces on the infinite-dimensional torus. Links to number…
This celebratory article contains a personal and idiosyncratic selection of a few open problems in discrete probability theory. These include certain well known questions concerning Lorentz scatterers and self-avoiding walks, and also some…