Related papers: Dennis Sullivan: Mathematics and physics; manifold…
The article surveys published and not yet published results about moduli spaces of algebraic surfaces.
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This book is the final version of a course on algorithmic information theory and the epistemology of mathematics and physics. This is camera-ready copy prepared for publication as a book, but at the last minute I decided to publish it…
Here I will review the theoretical results that have been obtained for spin glasses. I will concentrate my attention on the predictions of the mean field approach in three dimensional systems and on its numerical and experimental…
{\bf Abstract.} The present article is an essay about mathematical intuition and Artificial intelligence (A.I.), followed by a guided excursion to a well-known open problem. It has two objectives. The first is to reconcile the way of…
The article is taken out.
Without attempting to summarize the vast field of statistical mechanics, we briefly mention some of the progress that was made in areas which have enjoyed Barry Simon's interests. In particular, we focus on rigorous non-perturbative results…
This is the first part of a series of articles where we are going to develop theory of valuations on manifolds generalizing the classical theory of continuous valuations on convex subsets of a linear space. In this article we still work…
In this expository note, we discuss a ``balls-and-urns'' probability puzzle posed by Daniel Litt.
The linear isometries between weighted Banach spaces of continuous functions are considered. Some of well known theorems on isometries between spaces of continuous functions are proved and stated, but all they are in an appropriate form. In…
Astrophysics is a social enterprise exemplified here by the Dark Energy Survey (DES) which completed its fieldwork in 2019 after 16 years of preparation and observation, while data analysis continues. Society funds astrophysics on a grand…
David Mumford made groundbreaking contributions in many fields, including the pure mathematics of algebraic geometry and the applied mathematics of machine learning and artificial intelligence. His work in both fields influenced my career…
We obtain precise estimates, in terms of the measure of balls, for the Besov capacity of annuli and singletons in complete metric spaces. The spaces are only assumed to be uniformly perfect with respect to the centre of the annuli and…
This review article is the second part of the project ``Selected Topics of Social Physics". The first part has been devoted to equilibrium systems. The present part considers nonequilibrium systems. The style of the paper combines the…
This is a former PhD student's take on his teacher's scientific philosophy. I describe a set of 'principles' that I believe are conducive to good applied mathematics, and that I have learnt myself from observing Hans van Duijn in action.
An increasingly important area of interest for mathematicians is the study of Abelian differentials. This growing interest can be attributed to the interdisciplinary role this subject plays in modern mathematics, as various problems of…
This is a short review on the applications of Lieb-Robinson bounds for a general readership of mathematical physicists.
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…
The past decade has seen tremendous progress in our understanding of the behaviour of many probabilistic models at or near their "critical point". On the 5th of July 2022, Hugo Duminil-Copin was awarded the Fields medal for the crucial role…
This manuscript has been withdrawn by the author. Some of the material has been included in the manuscript 'Embedded Monopoles' at hep-th/0106254.