Related papers: The Work of John Tate
This paper, to appear in the ``Notices of the AMS'' 2024, is a modified version of a text already appeared in this journal, Feb. 2007 after a first publication in French, in ``La Gazette des Math{\'e}maticiens'' 97 (2003) on the occasion of…
This article is a draft of a book chapter of the book entitled "Quantum Percolation and Breakdown", to appear 2008.
This paper includes notes to accompany a reading of Thue's 1914 paper "Probleme uber Veranderungen von Zeichenreihen nach gegebenen Reglen", along with a translation of that paper. Thue's 1914 paper is mainly famous for proving an early…
This survey paper aims at providing a "literary" anthology of mathematical morphology on graphs. It describes in the English language many ideas stemming from a large number of different papers, hence providing a unified view of an active…
The main object of this paper is to present generalizations of gamma, beta and hypergeometric functions. Some recurrence relations, transformation formulas, operation formulas and integral representations are obtained for these new…
To appear in Encyclopedia of Mathematical Physics, published by Elsevier in early 2006. Comments/corrections welcome. The article surveys topological aspects in gauge theories.
This article aims at clarifying the language and practice of scientific experiment, mainly by hooking observability on calculability.
The rapid growth of scholarly literature makes it increasingly difficult for researchers to keep up with new knowledge. Automated tools are now more essential than ever to help navigate and interpret this vast body of information.…
The definition of negation has to be referred to the totality of a theory and at last to what is defined as the organization of a scientific theory; in other words, the definition of negation is of a structural kind, rather than of an…
This paper constitutes a background to the paper 'Quantum mechanics as "space-time statistical mechanics"?', arXiv:quant-ph/0501133, presented previously by the author. But it is also a free-standing and self-contained paper. The purpose of…
The essential elements in my way of fitting the kappa reviewed. A number of incorrect claims made by Takamatsu are clarified and corrected.
We give a selection of major open problems involving selective properties, diagonalizations, and covering properties for sets of real numbers. This is a revision of the version published as a chapter in the book \textbf{Open Problems in…
In the recent years, we have linked a large corpus of formal mathematics with automated theorem proving (ATP) tools, and started to develop combined AI/ATP systems working in this setting. In this paper we first relate this project to the…
This is an expanded version of my Shaw Prize Lecture delivered at the Chinese University of Hong Kong.
Perhaps the most important reason to understand the deep history of a field is that it is the right thing to do.
Telegraphic notes on the historical bibliography of the Gamma function and Eulerian integrals. Correction to some classical references. Some topics of the interest of the author. We provide some extensive (but not exhaustive) bibliography.…
We examine carefully the rationale underlying the approaches to belief change taken in the literature, and highlight what we view as methodological problems. We argue that to study belief change carefully, we must be quite explicit about…
This paper explores a dual score system that simultaneously evaluates the relative importance of researchers and their works. It is a modification of the CITEX algorithm recently described in Pal and Ruj (2015). Using available publication…
Expanding upon recent work, a new class of $A$-functions is introduced that can be viewed as an appropriate generalization of the class of regular $A$-functions, the class of structured $A$-functions, and the class of perfect $A$-functions.…
This document aims to give a self-contained account of the parts of abelian group theory that are most relevant for algebraic topology. It is almost purely expository, although there are some slightly unusual features in the treatment of…