Related papers: The work of James Maynard
This is a popular article about the work of James Maynard, 2022 Fields medalist.
Laudation delivered at the International Congress of Mathematicians in Berlin following the award of the Fields Medal to Richard Borcherds.
This is my laudation for Scholze's Fields medal 2018.
Andrei Okounkov received the Fields Medal at the ICM 2006 in Madrid "for his contributions bridging probability, representation theory and algebraic geometry". This is a brief account of his work.
Laurent Lafforgue has been awarded the Fields Medal for his proof of the Langlands correspondence for the full linear groups $\mathop{\rm GL}\nolimits_{r}$ ($r\geq 1$) over function fields. This article is a brief introduction to the…
We give a short appreciation of Robin Milner's seminal contributions to the theory of concurrency.
An overview of the accomplishments of constructive quantum field theory is provided.
We survey a decade worth of work pertaining to the nodal structures of random fields, with emphasis on the transformative techniques that shaped the field.
We summarize some of the main ideas and results around symplectic field theory, from its early inception up to recent and ongoing developments.
This is a report on the work of Robert Langlands, following his award of the Abel Prize in 2018. It includes his contributions to the general areas of Representation Theory, Automorphic Forms, Number Theory and Arithmetic Geometry. We have…
We construct small models of number fields and deduce a better bound for the number of number fields of given degree and bounded discriminant.
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…
We give a short appreciation of Mumford's work on the moduli of varieties by putting it into historical context. By reviewing earlier works we highlight the innovations introduced by Mumford. Then we discuss recent developments whose…
We give a proposal for future development of the model theory of valued fields. We also summarize some recent results on p-adic numbers.
We prove some extensions of Andrews inequality.
This is a short obituary of Saunders Mac Lane (1909--2005).
In this article the discovery of the Jones Polynomial will be discussed, emphasizing the way in which it illustrated the remarkable unity between distinct parts of Mathematics, each with its own language, but initially without a dictionary.
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 give a rough description of the 'categories' formed by quantum field theories. A few recent mathematical conjectures derived from quantum field theories, some of which are now proven theorems, will be presented in this language.
This talk presents a short review of David Brink's most important achievements and of my own experience working with him.