The Fields Medal is widely regarded as the highest honour a young mathematician can attain and is especially hard to win because the medals are only awarded every four years to mathematicians under the age of forty. This year Oxford Mathematician James Maynard is one of four recipients for his "contributions to analytic number theory, which have led to major advances in the understanding of the structure of prime numbers and in Diophantine approximation."
James is recognised as one of the leading figures in the field of number theory. Much of his career has focused on the study of general questions on the distribution of prime numbers. His early research was on sieve methods and gaps between prime numbers and as a postdoctoral researcher in Montreal he developed a new sieve method for detecting primes in bounded length intervals, and settled a long-standing conjecture of Paul Erdős on large gaps between primes. Subsequently he showed the existence of infinitely many primes missing any given digit (for example, 7).
More recently, James has developed a growing interest in questions about Diophantine approximation, and in joint work with D. Koukoulopoulos he settled the Duffin-Schaeffer conjecture and dramatically improved upon the work of Schmidt concerning simultaneous approximation by rationals with square denominator. Most recently, improving on classical work of Bombieri, Friedlander and Iwaniec, he published a monumental series of works on the distribution of primes in residue classes which goes beyond what follows from the Generalised Riemann Hypothesis.
James Maynard grew up in Chelmsford, Essex and attended the local grammar school (King Edward VI Grammar School). He did his undergraduate studies at Queens' College, Cambridge before moving to Oxford to do a DPhil under the supervision of Roger Heath-Brown where he has spent much of his career to date. After graduation, he was a CRM-ISM fellow in Montreal, a Junior Research Fellow at Magdalen College, Oxford and a Clay Research Fellow based in Oxford. He is now a Professor of Number Theory in Oxford and a Supernumerary Fellow at St John's College.
For his research in number theory, James has been awarded the SASTRA Ramanujan prize, the LMS Junior Whitehead prize, an EMS Prize, the Compositio prize and the AMS Cole Prize. His research was the focus of an AMS current events bulletin and a séminaire Bourbaki, and he was an invited speaker at the 2018 ICM.
The other three winners of the 2022 Fields medals are Hugo Duminil-Copin from the Université de Genève, June Huh from Princeton University (also a former Clay Research Fellow) and Maryna Viazovska from École Polytechnique Fédérale de Lausanne (EPFL).
Watch James discuss the award, his work and where he gets his inspiration in this short interview.
The Rising Talents Programme is designed to provide flexible and practical financial support, alongside tools and wider support, for early career women scientists to pursue their research. Five grants are awarded to outstanding women postdoctoral scientists in the fields of Physical Science, Engineering, Mathematics and Computing, Life Science, and Sustainable Development. These fully flexible Fellowships are each worth £15,000.
Bernadette's work develops techniques in topological data analysis (TDA) to study biological data, in particular dynamical networks and spatial data. Her research can be broadly categorised into three main groups: developing TDA techniques to answer biological questions arising from experimental data; developing novel data science methods based on TDA: and using TDA in combination with mechanistic models to link form and function in biological systems.
In her fellowship she will extend her work to mathematical models of tumour vasculature to enable predictions and investigate links between form and function. She will further develop techniques based on persistent homology to quantify heterogeneity in cancer tissue images and develop novel biomarkers for patient stratification, disease phenotyping, treatment prediction, and treatment scheduling. Ultimately, she hopes to make persistent homology biomarkers standard for cancer diagnosis and prognosis.
Bernadette is a Postdoctoral Research Associate in the Centre for Topological Data Analysis in Oxford. She has degrees in Molecular Medicine and also Mathematics (Major) and German Language and Literature Studies (Minor). She did her PhD in the Mathematical Institute, Oxford, (Lincoln College).
Congratulations to Oxford Mathematician Ehud (Udi) Hrushovski who is the joint winner of this year's Shaw Prize in Mathematical Sciences for his "remarkable contributions to discrete mathematics and model theory with interaction notably with algebraic geometry, topology and computer sciences". He shares the prize with Noga Alon, Professor of Mathematics at Princeton University.
Udi is Merton Professor of Mathematical Logic at the University of Oxford and a Fellow of Merton College, Oxford. He studied in the University of California, Berkeley, and worked in Princeton, Rutgers, MIT and Paris and for twenty five years at the Hebrew University in Jerusalem before coming to Oxford.
Udi's work is concerned with mapping the interactions and interpretations among different mathematical worlds. Guided by the model theory of Robinson, Shelah and Zilber, he investigated mathematical areas including highly symmetric finite structures, differential equations, difference equations and their relations to arithmetic geometry and the Frobenius maps, aspects of additive combinatorics, motivic integration, valued fields and non-archimedean geometry. In some cases, notably approximate subgroups and geometric Mordell-Lang, the metatheory had impact within the field itself, and led to a lasting involvement of model theorists in the area. He also took part in the creation of geometric stability and simplicity theory in finite dimensions, and in establishing the role of definable groups within first order model theory. He has co-authored papers with 45 collaborators and has received a number of awards including the Karp, Erdős and Rothschild prizes and the 2019 Heinz Hopf prize.
The Shaw Prize is an annual award first presented by the Shaw Prize Foundation in 2004. Established in 2002 in Hong Kong it honours living individuals who are currently active in their respective fields and who have recently achieved distinguished and significant advances, who have made outstanding contributions in academic and scientific research or applications, or who in other domains have achieved excellence.
The Shaw Prize consists of three annual prizes: Astronomy, Life Science and Medicine, and Mathematical Sciences, each bearing a monetary award of US$1.2 million. This will be the eighteenth year of the awards.
Udi becomes the fifth UK-based mathematician to win the prize. All five (Andrew Wiles, Richard Taylor, Simon Donaldson, Nigel Hitchin being the other four) have held faculty positions at Oxford.
Fernando Alday (pictured left) is an Argentinean Theoretical Physicist and Mathematician, Rouse-Ball Professor of Mathematics and Head of the Mathematical Physics Group in Oxford, and a fellow of Wadham College. He did his undergraduate at Centro Atomico Bariloche, Argentina, and his DPhil at SISSA, Italy, under the supervision of Edi Gava and Kumar Narain. He joined Oxford in 2010, after doing Postdocs at Utrecht University in the Netherlands and at the Institute for Advanced Study in the US.
Fernando is well-known for the development of mathematical tools to understand fundamental questions in Quantum Field Theory and Quantum Gravity. His most important contributions involve surprising dualities among different theories and observables in high energy theoretical physics. One of these dualities relates scattering amplitudes to minimal surfaces/soap bubbles in anti-de-Sitter space, while another, known as the AGT correspondence, relates correlation functions in a two-dimensional theory to the spectrum of four-dimensional gauge theories. More recently, Fernando has been developing mathematical tools to compute string and M-theory amplitudes in curved space-time, a subject still in its infancy.
Alain Goriely is a mathematician with broad interests in mathematical methods, mechanics, sciences, and engineering. He is well known for his contributions to fundamental and applied solid mechanics, and, in particular, for the development of a mathematical theory of biological growth, culminating with his seminal monograph The Mathematics on Mechanics of Biological Growth (2017).
He received his PhD from the University of Brussels in 1994 where he became a lecturer. In 1996, he joined the University of Arizona where he established a research group within the renowned Program of Applied Mathematics. In 2010, he joined the University of Oxford as the inaugural Statutory Professor of Mathematical Modelling and fellow of St. Catherine’s College. He is currently the Director of the Oxford Centre for Industrial and Applied Mathematics (OCIAM).
In addition, Alain enjoys scientific outreach based on problems connected to his research, including tendril perversion in plants, twining plants, umbilical cord knotting, whip cracking, the shape of seashells, brain modelling. He is the author of a Very Short Introduction to Applied Mathematics (2017).
Oxford Mathematics now has 31 Fellows of the Royal Society among its current and retired members: John Ball, Bryan Birch, Martin Bridson, Philip Candelas, Marcus du Sautoy, Artur Ekert, Alison Etheridge, Ian Grant, Ben Green, Roger Heath-Brown, Nigel Hitchin, Ehud Hrushovski, Ioan James, Dominic Joyce, Jon Keating, Frances Kirwan, Terry Lyons, Philip Maini, Vladimir Markovic, Jim Murray, John Ockendon, Roger Penrose, Jonathan Pila, Graeme Segal, Endre Süli, Martin Taylor, Ulrike Tillmann, Nick Trefethen, Andrew Wiles, and Fernando and Alain of course.
Congratulations to Oxford Mathematicians Roisin Stephens and Giulia Laura Celora who won prizes for their talks at this year's British Applied Mathematics Colloquium (BAMC) and to Anna Berryman who was a prize winner in the poster category.
The BAMC is an annual event dating back to 1959 that has a central place in the UK Applied Mathematics calendar. It is one of the first places where PhD students and Early Career Researchers present their work, and where mathematicians across all career stages have a chance to actively interact with each other. It was held in person this year from 11-13 April at Loughborough University.
Congratulations to Oxford Mathematics and Worcester College undergraduate Ellen who was a joint winner of the British Society for the History of Mathematics Undergraduate Essay Prize for her essay 'The "analysis" of a century: Influences on the etymological development of the word "analysis" in a mathematical context to 1750'.
Ellen says of her work: "I took the History of Maths module as I have always enjoyed hearing about how people and societies have thought about the concepts that we take for granted. I found that learning and exploring the original mathematical texts helped me to contextualise my place as an undergraduate in the overall mathematical story!
"My essay, which was adapted from the essay I submitted for my final coursework, explores the evolving meaning of the word ‘analysis’ in a mathematical context from Oughtred to Euler. It delves into themes including the geometric-analytic distinction and how the nature of mathematical texts, as well as their contents, has helped mathematical ideas to stick."
Ellen completed her degree this summer. Below, you can watch a lecture from the History of Mathematics course she took, one of the many undergraduate lectures we are making available to give an insight in to mathematical life in Oxford.
Oxford Mathematician Frances Kirwan has been awarded the Sylvester Medal 2021 "for her research on quotients in algebraic geometry, including links with symplectic geometry and topology, which has had many applications."
The Sylvester Medal is awarded annually for an outstanding researcher in the field of mathematics. The award was created in memory of the mathematician James Joseph Sylvester who was Savilian Professor of Geometry at the University of Oxford in the 1880s, a post now held by Frances Kirwan (the Savilian celebrated its 400th anniversary in 2019). The Sylvester medal was first awarded in 1901. It is of bronze and is accompanied by a gift of £2,000.
Frances's specialisation is algebraic and symplectic geometry, notably moduli spaces in algebraic geometry, geometric invariant theory (GIT), and the link between GIT and moment maps in symplectic geometry.
Frances has received many honours including being elected a Fellow of the Royal Society in 2001 (only the third female mathematician to attain this honour), and President of the London Mathematical Society from 2003-2005. She was made a Dame Commander of the Order of the British Empire in 2014.
On receiving the award Frances said: "I am honoured to receive this award, especially as it is named after one of my predecessors as Savilian Professor, James Joseph Sylvester, whose work over a hundred years ago on what is today called invariant theory laid the foundations for my own work on geometric invariant theory."
Four Oxford Mathematicians have been awarded 2021 London Mathematical Society (LMS) Prizes. Ehud Hrushovski is awarded a Pólya Prize, Endre Süli is awarded the Naylor Prize and Lectureship, and Patrick Farrell and Stuart White receive Whitehead Prizes.
Udi Hrushovski's work is concerned with mapping the interactions and interpretations among different mathematical worlds. Endre's research is concerned with the analysis of numerical algorithms for the approximate solution of partial differential equations and the mathematical analysis of nonlinear partial differential equations in continuum mechanics. Patrick works on the numerical solution of partial differential equations, while Stuart's research focuses on operator algebras, a branch of functional analysis with connections to many other branches of pure mathematics.
The Athena Swan Charter is a framework which is used across the globe to support and transform gender equality within higher education (HE) and research.
In 2013 the Mathematical Institute received an Athena Swan Bronze Award for its work in addressing the issue of gender equality in its subject and working environment and, as a result of our work over the next four years, in 2017 we received the Silver Award. This year that Silver has been renewed and reflects the work put in as we strive for gender equality in a subject that, while predominantly still male, is becoming more balanced.
What have we done?
- We have Increased gender diversity across most student/staff groups, with female postgraduate numbers almost doubling. Given that these are the faculty of the future, In Oxford and elsewhere, this is very encouraging. We will continue to work on providing an environment that encourages those students to continue to progress in their careers.
- We are pleased with the ongoing success of our recent, prestigious Hooke and Titchmarsh Postdoctoral Research Fellowships, which attract a high number of women and provide an exceptional springboard into an independent academic career.
- We continue to work hard to engage and encourage young school-age female mathematicians. It All Adds Up, where we bring female school pupils together to meet other keen young mathematicians, is just one successful example. We are approaching 30% female undergraduate intake, in line with the number of female high-school students studying Further Maths at 'A' Level.
Charters such as Athena Swan work best when they make you think about what you do rather than being an end in themselves. That has been perhaps the most successful part of Athena Swan for us. We are integrating it into our strategic priorities and intertwining it with, for example, our Race Equality action plan.. Mathematics is a subject that had a lot of ground make up, but we and the wider mathematical world are making meaningful progress.
There are plenty of awards and prizes for senior mathematicians and scientists. But just as important, and maybe more so, are the awards for those just starting out.
SIGACT (Special Interest Group on Algorithms and Computation Theory) is an international organisation that fosters and promotes the discovery and dissemination of high quality research in theoretical computer science. The Danny Lewin Best Student Paper award is presented by SIGACT each year at the ACM Symposium on Theory of Computing.
Oxford DPhil Mathematician Zachary's winning paper is entitled “Separating Words and Trace Reconstruction.” A deterministic finite automaton is one of the most basic computational models in theoretical computer science. Telling two strings apart is one of the most basic computational tasks. In this paper, progress is made on an old problem of how efficiently one can tell two strings apart with a deterministic finite automaton. The proof methods surprisingly involve complex analysis and connections to other fundamental problems.
