相关论文: The masterpieces of John Forbes Nash Jr

This is my article on Tate's work for the second volume in the book series on the Abel Prize winners. True to the epigraph, I have attempted to explain it in the context of the "great reformulation".

Given the present state of work in natural language processing, this address argues first, that advance in both science and applications requires a revival of concern about what language is about, broadly speaking the world; and second,…

Work in progress concerning alternative formalizations of arithmetic.

This note is about a little extension of Nash's embedding theorem in the case of complete manifolds.

We strengthen certain known results saying that separately regular functions are rational and separately Nash functions are semialgebraic. The approach presented here unifies and highlights the similarities between the two problems.

This survey article collects a few of my favorite open problems of Branko Gr\"{u}nbaum.

The aim of this note is to survey the factorizations of the Fibonacci infinite word that make use of the Fibonacci words and other related words, and to show that all these factorizations can be easily derived in sequence starting from…

This document contains a description of several of my papers, including remarks on history and connection with subsequent work. It also contains some new results and conjectures.

Invited book review, as submitted to the electronic database MathSciNet, of the 2006 book by Tom Siegfried, "A beautiful math. John Nash, game theory, and the modern quest for a code of nature" (Joseph Henry Press, Washington, DC).

I present some reminiscences, both personal and scientific, over a lifetime of admiration of, and friendship with, one of the Grandmasters of our subject.

This is a write-up of introductory remarks that I made at the UIC conference in honor of Lawrence Ein's 60th birthday. It presents an informal survey of some of Ein's work, interspersed with stories and reminiscences.

In his previous paper, the author has defined a higher version of the Nash blowup and considered it a possible candidate for the one-step resolution. In this paper, we will introduce another higher version of the Nash blowup and prove that…

New cases of the multiplicity conjecture are considered.

An obituary of J.R. Dorfman. The focus is on his scientific career and on his many important publications.

This note revisits some majorization inequalities for eigenvalues, special attention is given to an elegant theorem of Hiroshima. An extension of the special case of Hiroshima's theorem is presented. Some discussion and open problems are…

In the 1960s, John Nash proposed a method to resolve singularities. Five decades of encouraging results could not prevent an unexpected ending: the method does not work in general. In this note (written in Spanish), we tell the story of the…

This is part of an unpublished work in collaboration with Ralph Kenna. It was probably not mature enough at the time it was submitted more than ten years ago and it was rejected by the editors, but some of the ideas had later been published…

This is a reply to Muff, S. et al. (2022) Rewriting results sections in the language of evidence, Trends in Ecology & Evolution 37, 203-210.

In the first part of this paper I will describe my work together with Lars and in the second part I will give a look at some of Lars's oldest papers.

In the past few decades there has been a good deal of papers which are concerned with optimization problems in different areas of mathematics (along 0-1 words, finite or infinite) and which yield - sometimes quite unexpectedly - balanced…