OUP Fields Medallists
<div><span style="font-size:16px;">Atiyah spent thirty years living and working at Oxford University from 1961 to 1990, in a time when the Mathematical Institute was expanding from a select group of intellectuals to a large network of colleagues encouraging national and international collaboration. This new mathematical scene and time spent at the Institute of Advanced Study at Princeton University allowed Atiyah to collaborate with many of the brightest mathematical minds and eventually led to the work recognized by the Medal. </span></div> www.oxfordscholarship.com Some personal reminiscences - Oxford Scholarship
<div><span style="font-size:16px;">Publishing his first maths paper at the age of 16, Bombieri has taught and lived primarily in Italy and the US. His research in number theory, algebraic geometry, and mathematical analysis has earned him a number of accolades over the years. Together with Ennio De Giorgi and Enrico Giusti, he solved Bernstein’s problem. </span></div> doi.org Abstract. Krishnapur et al. [15] studied the length of the fluctuations of nodal lengths of random Laplace eigenfunctions on the standard 2-torus. A key step i
<div><span style="font-size:16px;">Yau began researching the mathematical objects known as complex manifolds predicted by mathematician Eugenio Calabi, which were considered firstly from a purely mathematical perspective. Yau looked at them from a physical perspective and in relation to the theory of general relativity, leading physicists to be able to show string theory as a viable candidate for a unified theory of nature. </span></div> global.oup.com Nigel Hitchin is one of the world's foremost figures in the fields of differential and algebraic geometry and their relations with mathematical physics, and he has been Savilian Professor of Geometry at Oxford since 1997.
<div><span style="font-size:16px;">After gaining a DPhil from Oxford University in 1983, he launched into working on applying mathematical analysis to problems of geometry, using traditional calculus to show connection between the geometry and the arithmetic. This research has helped to provide models for recent developments in manifold topology, Riemannian geometry, and diverse applications in mathematical physics.</span></div> www.oxfordscholarship.com Holomorphic functions - Oxford Scholarship
<div><span style="font-size:16px;">The results from his work that earned him the Medal has been extended to dimensions higher than three and is called the Mori programme, which is currently an active field of algebraic geometry research. Mori was elected as the president of the International Mathematical Union, becoming the first head to represent East Asia. </span></div> global.oup.com Nigel Hitchin is one of the world's foremost figures in the fields of differential and algebraic geometry and their relations with mathematical physics, and he has been Savilian Professor of Geometry at Oxford since 1997.
<div><span style="font-size:16px;">Witten became the first physicist to ever be awarded the Medal. Witten coined the term </span><i><span style="font-size:16px;">topological quantum field theory </span></i><span style="font-size:16px;">for a type of physical theory where expectation values of observable quantities provide information about the topology of spacetime. One of the assertions he’s most known for is that the physical theory, the Chern-Simons theory, can provide a framework for understanding the mathematical theory of knots and 3-manifolds. </span></div> www.oxfordscholarship.com Two Lectures on the Jones Polynomial and Khovanov Homology - Oxford Scholarship
<div><span style="font-size:16px;">Since winning the Fields Medal, Bourgain has used his wide-ranging interests to work on problems and solutions that span Banach spaces, harmonic analysis, ergodic theory, and spectral problems. His sum-product theory in algebra has had far-reaching consequences, and has even been able to make connections to the Kakeya needle problem. </span></div> doi.org Jean Bourgain; Approximation of solutions of the cubic nonlinear Schrödinger equations by finite-dimensional equations and nonsqueezing properties, Internation
<div><span style="font-size:16px;">Lions was the first mathematician to provide a solution with proof of the Boltzmann equation, left unsolved since its formulation 1872. Since there currently is no core theory on nonlinear partial differential equations, understanding in this field has come mainly through the study of particular equations in applications. Lions has spent much of his career solving these equations. </span></div> global.oup.com One of the most challenging topics in applied mathematics over the past decades has been the developent of the theory of nonlinear partial differential equations. Many of the problems in mechanics, geometry, probability, etc lead to such equations when formulated in mathematical terms.
<div><span style="font-size:16px;">Basing his early research in Banach spaces and using combinatorial tools, he constructed a Banach space with almost no symmetry, though he is more known for his work in arithmetic combinatorics on the Gowers norms. Not only are his contributions great in the academic sphere, but Gowers has also worked to popularize mathematics, using the Polymath Project to increase engagement with maths while also writing accessible study tools for young students. </span></div> www.veryshortintroductions.com 8. Some frequently asked questions - Very Short Introductions
<div><span style="font-size:16px;">Okounkov has worked on the representation theory of infinite symmetric groups, the statistics of plane partitions, and the quantum cohomology of the Hilbert scheme of points in the complex plane. He has also produced work that proves the conjecture of Baik, Deift, and Johansson. </span></div> doi.org Abstract. We prove the conjecture of Baik, Deift, and Johansson, which says that with respect to the Plancherel measure on the set of partitions λ of n, the ro
<div><span style="font-size:16px;">Proven to be a young maths whiz, Tao has been solving problems in a variety of subfields of maths since the early nineties. His work with Ben Green on arithmetic progressions in the set of primes first put him in the spotlight, while still spending time on topics such as the Kakeya problem. Having won a gold medal at the International Mathematical Olympiads as a kid, he also regularly creates exercises to help those training for the event. </span></div> global.oup.com Authored by a leading name in mathematics, this engaging and clearly presented text leads the reader through the various tactics involved in solving mathematical problems at the Mathematical Olympiad level. Covering number theory, algebra, analysis, Euclidean geometry, and analytic geometry, Solving Mathematical Problems includes numerous exercises and model solutions throughout.
<div><span style="font-size:16px;">Working in the area of dynamics, Lindenstrauss’ work looks particularly at ergodic theory and its application in number theory. He’s made major progress on the Arithmetic Quantum Unique Ergodicity conjecture. He counts several Fields Medallists amongst his co-authors. </span></div> doi.org Abstract. We classify locally finite invariant measures and orbit closure for the action of the mapping class group on the space of measured laminations on a s
<div><span style="font-size:16px;">Receiving his PhD from Caltech, much of Smirnov’s work has been on in the statistical physics field of percolation theory. He proved Cardy’s formula for critical site percolation on the triangular lattice and deduced conformal invariance from that. His research into this area has led to a fairly complete theory for percolate on the triangular lattice.</span></div> doi.org Abstract. We prove that unicritical polynomials with metrically generic combinatorics of the critical orbit satisfy the Collet-Eckmann conditions. Here metrica
<div><span style="font-size:16px;">Bhargava started his career at Harvard University, focusing his PhD on resolving the Polya conjecture by devising a generalization of the factorial function, known as the Bhargava factorial. Some of his other accomplishments include proofs of the 15 theorem, extending the theorem to also include number sets that are odd and prime, and the 290 theorem with Jonathan Hanke. </span></div> doi.org Abstract. Using Serre's mass formula [15] for totally ramified extensions, we derive a mass formula that counts all (isomorphism classes of) étale algebra exte
<div><span style="font-size:16px;">Mirzakhani is particularly known for being able to prove the long-standing conjecture that William Thurston’s earthquake flow on Teichmüller space is ergodic in addition to that on Riemann surfaces. In her career, she has built on the work of Edward Witten and Maxim Kontsevich, providing new proofs of their formulae on the intersection numbers of tautological classes on moduli space. </span></div> doi.org Maryam Mirzakhani; Ergodic Theory of the Earthquake Flow, International Mathematics Research Notices, Volume 2008, 1 January 2008, rnm116, https://doi.org/10.1

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