TY - JOUR
AB - BORIS ZILBER Pólya Prize 2015 The Pólya Prize is awarded to PROFESSOR BORIS ZILBER of the University of Oxford for his visionary contributions to model theory and its applications. Boris Zilber has been a principal architect of the geometrisation of model theory, which has transformed the subject and its relationships with other disciplines in recent years. His work has elucidated the important role played by ‘dimension’ notions and the ‘geometries’ they support in determining model-theoretic properties of a structure. Exploring this role, he has made fundamental contributions to many areas of pure and applied model theory. In particular, the theory of Zariski geometries, initiated by Hrushovski and Zilber, has been further developed by Zilber, his collaborators, students, and others, with applications in Diophantine, complex and non-commutative geometry, and mathematical physics. A central idea informing Zilber's work is the ‘model-theoretic perfection’ of classical structures in mathematics. Revisiting a method of construction due to Hrushovski and combining it with deep ideas in pure model theory due to Shelah, Zilber constructed a ‘perfect exponential function’ that satisfies Schanuel's Conjecture, as well as other properties conjectured but not known for the classical complex exponential, and that has excellent model-theoretic properties. Comparing Zilber's exponential function with the complex exponential function is a rich area of research. Zilber's highly original ideas have led him to formulate several influential conjectures in model theory and Diophantine geometry. His over-arching vision has profoundly influenced the face of model theory, and has been a source of inspiration to mathematicians in the UK and beyond. KEITH BALL Shephard Prize 2015 The Shephard Prize is awarded to PROFESSOR KEITH BALL, FRS, of the University of Warwick for his many beautiful results in geometry (particularly the geometry of convex regions), number theory, and probability theory. Ball's famous ‘cube slicing theorem’ proves the following simple-to-state and intuitive fact: every central hyperplane section of the cube $$[-\tfrac {1}{2},\tfrac {1}{2}]$$ has $$(n-1)$$-dimensional area at most $$\sqrt {2}$$. This bound is attained when the hyperplane in question is orthogonal to the vector $$(1, 1, 0, \ldots , 0)$$. Despite the elementary statement, Ball's proof is not elementary, relying on a subtle Fourier-analytic argument. A consequence of this was the first ‘natural’ counterexample to the Busemann–Petty problem. In 1956, Busemann and Petty asked whether, if $$K$$ and $$L$$ are two centrally symmetric $$n$$-dimensional convex bodies and if every $$(n-1)$$-dimensional central cross section of $$K$$ has larger volume than the corresponding cross section of $$L$$, does it follow that $$K $$ has larger volume than $$L$$? The answer is no, and indeed Ball's result shows that a counterexample is provided simply by taking a cube and a suitably scaled sphere, at least in dimension 10 or more. Another stunning geometric result of Ball is his so-called reverse isoperimetric inequality. Given a convex body $$K$$ of unit volume in $$\mathbb {R}^n$$, the isoperimetric inequality states that the surface area of $$K$$ is at least the surface area of a Euclidean ball of unit volume. It is hopeless to expect an upper bound, since $$K$$ could be extremely flat, in which case it would have very large surface area. However, if one is allowed to apply an affine transformation to $$K$$, the story is completely different: Ball showed that every $$K$$ has an affine image of unit volume whose surface area is at most that of the $$n$$-dimensional simplex of unit volume. Ball, in joint work with Rivoal, proved a famous result in number theory. Writing   \[ \zeta(m) = 1 + \frac{1}{2^m}+\frac{1}{3^m}+ \cdots \] for the Riemann $$\zeta $$-function, it is known that if $$m$$ is an even positive integer then $$\zeta (m)$$ is a rational multiple of $$\pi ^m$$, and hence is irrational. The values of $$\zeta $$ at odd arguments, $$\zeta (3)$$, $$\zeta (5)$$ and so on are much more mysterious, and in particular it is not known whether $$\zeta (5)$$ is irrational. However, Ball and Rivoal did manage to show that infinitely many of these numbers are irrational. Finally we mention a beautiful result of Ball in probability theory, obtained in joint work with Artstein, Barthe and Naor. Establishing a conjecture of Shannon from the 1940s, they proved that if $$X_1, X_2, \ldots $$ are i.i.d. random variables with variance 1, then the entropy of   \[ \frac{1}{\sqrt{n}} (X_1 + \cdots + X_n) \] is a monotone increasing function of $$n$$, showing that the central limit theorem is driven by an analogue of the second law of thermodynamics. ROBERT MACKAY Senior Whitehead Prize 2015 The Senior Whitehead Prize is awarded to PROFESSOR ROBERT MACKAY, FRS, of the University of Warwick for his outstanding contributions to research in dynamical systems and its applications. Robert MacKay has made many important contributions to dynamical systems theory and its applications. In particular, his work has contributed greatly to our understanding of the structure of phase space in two-degrees-of-freedom Hamiltonian systems. Notably, he developed a theory in terms of renormalisation operators that explains the way in which the celebrated KAM tori break down, and he interpreted Mather's action difference as a flux through the gaps of the resulting cantori. These results have been applied to plasma physics, chemical reaction theory, advection by fluid flows and interpretation of the ionisation of highly excited atoms. Other highlights of his research include: a proof of existence of spatially localised time-periodic oscillations in networks of oscillators (discrete breathers) and analysis of their stability, interaction and mobility; construction and proof of a mechanical example of an Anosov system; construction of indecomposable spatially extended deterministic dynamical systems exhibiting more than one space-time phase; proof of existence of Poincaré's second species periodic orbits and chaotic counterparts; and application of Hamiltonian theory to explain the stability diagrams of water waves and vortex streets. A remarkably creative and prolific mathematician, in addition to the broad impact of his research, he has made an outstanding contribution to the mathematical community, in particular, through his role in developing modern applied mathematics and (more recently) complexity science, and through his presidency of the Institute of Mathematics and its Applications. STEPHEN CHAPMAN Naylor Prize and Lectureship in Applied Mathematics 2015 The Naylor Prize and Lectureship is awarded to PROFESSOR STEPHEN JONATHAN CHAPMAN of the University of Oxford for his outstanding contributions to modelling and methods development in applied mathematics. Modelling and solving scientific problems using mathematics is as much an art as it is a science. It requires a delicate balance between good taste, mathematical mastery, technical skills, and in-depth understanding of the underlying scientific question. Chapman has demonstrated through his scientific career the perfect combination of skills in modelling, developing methods, and finding elegant solutions to outstanding problems. Chapman's expertise spans the development and application of methods of applied mathematics (asymptotic series, complex function theory, PDEs) to a number of fundamental problems both in the theory of differential equations (ODEs, PDEs, stochastic, pattern formation), in science (superconductivity, hydrodynamics, mathematical biology), in engineering (dislocations, batteries) and in industry. For example, his mathematical work on the theory of superconductivity provides a systematic basis to understand and solve a number of key problems such as the destruction of superconductivity by a magnetic field, the time-dependent nucleation of superconductivity, the motion for vortices in type II superconductors, and to explain pinning through impurities. In recent work, Chapman has developed a new theory of asymptotic homogenisation for multiscale and multiphysics nonlinear problems applicable to engineering and biology as well as new theoretical and computational methods for the multiscale analysis of stochastic reaction–diffusion equations with application to cellular biology and chemical physics. In addition to his research, Chapman has a profound influence on the applied mathematics community through his leadership in the UK and internationally, his lecturing gifts, and his crucial role in the promotion of industrial mathematics. The Berwick Prize is awarded to PIERRE-EMMANUEL CAPRACE of Université Catholique de Louvain and NICOLAS MONOD of École Polytechnique Fédérale de Lausanne in recognition of their papers ‘Isometry groups of non-positively curved spaces: structure theory’ and ‘Isometry groups of non-positively curved spaces: discrete subgroups’ (J. Topol. 2 (2009) 661–700 and 701–746). These two 40-page papers contain many foundational and significant results advancing the state of the art in the field of CAT(0) geometry, and they facilitate extensive applications in geometry, topology, group theory and other related fields. They are the most highly-cited papers from the Journal of Topology. A CAT(0) space is a complete metric space that is non-positively curved in the sense of Alexandrov. The most classical examples are symmetric spaces of non-compact type but the wide applicability of the theory rests on the fact that there are also many natural singular examples, beginning with trees and Bruhat–Tits buildings of affine type. The work of Caprace and Monod involves a penetrating study of the isometry group Iso(X) of a CAT(0) space X. It significantly advances the state of the art. If X is proper, then Iso(X) is locally compact and allows one to consider lattices, that is, discrete subgroups of finite co-volume. In these papers Caprace and Monod extend the rich classical theory of lattices in semi-simple groups as well as extensions proved by Gromov and others. They prove product decomposition theorems (algebraic and geometric) in the spirit of de Rham; symmetric spaces and Euclidean buildings emerge beautifully from the condition that stabilisers at infinity act co-compactly on the interior. In a similar spirit, they prove that if G is a simple algebraic group over a local field acting continuously and co-compactly by isometries on X, and if X is geodesically complete, then X is the symmetric space or Euclidean building associated to G. And they go on to prove super-rigidity results, a geometric extension of the Borel density theorem, and extensions of Margulis-type arithmeticity theorems (starting without smooth structure!). These are remarkable papers that will provide inspiration long into the future! PETER KEEVASH Whitehead Prize 2015 A Whitehead Prize is awarded to PROFESSOR PETER KEEVASH of the University of Oxford for his work in combinatorics. Keevash has a large body of work that touches on several parts of combinatorics including extremal problems about hypergraphs, Ramsey theory and design theory. Many of his papers are tours de force illustrating exceptional command of subtle probabilistic methods in combinatorics, yet the end results are clean and relatively elementary. In joint work with Bohman, Keevash analysed the so-called triangle-free graph process. Here one starts with $$n$$ vertices and sequentially adds edges at random to form a graph. Each edge is chosen uniformly, subject to the condition that no triangle should be formed by the addition of the new edge. At some point this process terminates, and one is interested in what the final graph $$G$$ looks like (with high probability). Bohman and Keevash found an asymptotic for the number of edges in $$G$$, and also for its independence number. An immediate consequence of their result is the best lower bound currently known for the off-diagonal Ramsey number $$R(3,t)$$, the smallest number $$n$$ of vertices for which it is guaranteed that a red–blue colouring of the complete graph on $$n$$ vertices contains either a red triangle or a blue clique of size $$t$$. In a spectacular breakthrough, Keevash proved the existence of combinatorial designs for essentially all ‘allowable’ values of the parameters. Suppose we have integer parameters $$q, r$$ and $$\lambda $$. Let $$n$$ be a large integer. Then an $$(n, q, r, \lambda )$$-design is a collection of $$q$$-element subsets of $$\{1,\dots , n\}$$ with the property that every $$r$$-element subset of $$\{1,\dots , n\}$$ is a subset of precisely $$\lambda $$ of them. For example, an $$(n, 3, 2, 1)$$-design can be thought of as a collection of triangles on the vertex set $$\{1,\dots , n\}$$ such that each edge lies in precisely one of them. It is an easy exercise to see that such a design can exist only if $$\binom {q-i}{r-i}$$ divides $$\lambda \binom {n - i}{r - i}$$ for $$i = 0,1,\dots , r-1$$. Keevash's theorem establishes that this necessary condition is also sufficient, provided that $$n > n_0(q, r,\lambda )$$ is sufficiently large. To do this he introduces a subtle method, which he calls randomised algebraic constructions, involving a long sequence of random extensions of an initial algebraically-defined partial design ‘template’ followed by a cleanup. To illustrate just how significant an advance this is, we note that in the case $$\lambda = 1$$ (Steiner systems) it was not previously known if there are any of these designs at all with $$r \geq 6$$. JAMES MAYNARD Whitehead Prize 2015 A Whitehead Prize is awarded to DR JAMES MAYNARD of the University of Oxford for his spectacular results on gaps between prime numbers. Yitang Zhang famously proved in 2013 that there are infinitely many pairs of primes differing by at most 70 million. His method relied in part on some very deep estimates from algebraic geometry, as well as a complicated application of the machinery of bilinear forms in analytic number theory. Maynard (and independently Tao) provided a fresh approach to the problem by introducing a new class of sieve weights. This method is considerably more elementary than that of Zhang, to the extent that the whole proof could now be taught in a graduate course. Furthermore it leads to superior bounds, the current record (obtained by Maynard and others as part of the ‘Polymath’ project) having 70 million replaced by 246. Moreover, the Maynard–Tao method allows one to find clusters of $$m > 2$$ primes close together; in fact there are infinitely many $$x$$ such that there are $$m$$ primes in the interval $$[x, x + e^{Cm}]$$, for some constant $$C$$. In a further spectacular advance, Maynard applied his new sieve weights to make the first substantial improvement on the question of how large the gap between consecutive primes less than $$x$$ can be since work of Rankin in the 1930s, beating Rankin's lower bound by a function tending to infinity with $$x$$. The Hungarian mathematician Paul Erdös had offered 10,000 dollars — the most generous of the many prizes he offered for solving mathematical problems — for doing precisely this. In collaboration with Ford, Green, Konyagin and Tao (who independently solved Erdös's problem, though with more complicated methods and a weaker bound), Maynard has a preprint improving the Rankin bound by a factor of $$\log \log \log x$$. CHRISTOPH ORTNER Whitehead Prize 2015 A Whitehead Prize is awarded to PROFESSOR CHRISTOPH ORTNER of the University of Warwick for contributions to the mathematical foundations, development and implementation of the quasicontinuum method. The quasicontinuum method is probably the leading multiscale method that tries to express macroscale quantities like stress and free energy directly in terms of atomistic data, such as the positions and species of the atoms composing the material. The method gains simplification through the observation (requiring proof) that the positions of the atoms perturb smoothly a regular lattice in regions away from defects. A key challenge of the method is the treatment of the transition region between the fully atomistic region near the defect and the far-field region that perturbs a regular lattice. Ortner's approach is to base the development of the method on rigorous analysis. His main contributions have been to produce a mathematical framework for the error analysis of the quasicontinuum method that applies in more than one spatial dimension; explicit stability estimates for several versions of the quasicontinuum method; and a proof under reasonable hypotheses of the consistency (via the patch test) of an important family of quasicontinuum methods in two spatial dimensions. Ortner's work has introduced a clear mathematical structure that allows one to understand clearly the range of applicability of current results and the remaining challenges, thus attracting the interest of a broader community of mathematicians to this research area. MASON PORTER Whitehead Prize 2015 A Whitehead Prize is awarded to PROFESSOR MASON PORTER of the University of Oxford in recognition of his outstanding interdisciplinary contributions and in particular to the emerging field of network science, where he has combined unique analysis of biological, social and political data sets with novel methods for community detection and other forms of coarse graining. Mason Porter has made outstanding contributions in multiple areas of applied mathematics, including dynamical systems, nonlinear science, granular media, quantum mechanics, and in particular to the theory of network science. For instance, in the study of nonlinear waves, Porter demonstrated, through a beautiful combination of theory, numerics and experiments, the existence of intrinsic localized modes in granular crystals. In more recent work, Porter has become a world leader in the field of network science. Network science is the study of complex networks appearing in many different fields such as telecommunication, biological sciences and social sciences. It combines multiple mathematical and physical disciplines such as graph theory, statistics, and data mining. In this field, Porter has made influential contributions: he developed the first systematic method to detect communities in time-dependent and multiplex networks, proposed computational methods for validating the output of community-detection algorithms, and has conducted thorough studies of dynamical systems on networks. Porter applied community-detection and other coarse-graining methods successfully to brain networks, and to the social structure of universities and of the US Congress. He has also studied applications such as functional groups in protein–protein interaction networks and time-dependent correlations in foreign-exchange markets. In addition to his research, Porter is a consummate and diverse collaborator; he is an accomplished populariser of mathematics, maintaining a blog, contributing to scientific galleries and writing expository articles on topics from across nonlinear science. DOMINIC VELLA Whitehead Prize 2015 A Whitehead Prize is awarded to PROFESSOR DOMINIC VELLA of the University of Oxford for his spectacular contributions to the modelling of instability and interfacial phenomena in fluids and solids. In fluid and solid mechanics, there is an extremely rich and important panoply of behaviours that take place right at the boundary of structures and that can be observed in Nature: insects walk on water, gas bubbles float on liquids, thin elastic films delaminate or wrinkle, and wet hairs aggregate due to capillary interactions. Throughout his work, Vella has identified a number of fascinating problems of fluid–solid interactions for which he has provided beautiful mathematical treatments. In his early work, he described the dynamics of the ‘Cheerios effect’ by which floating bodies interact with each other, showing further that such interactions can cause objects to sink. He also studied important hydrodynamic effects associated with the storage of carbon in porous media and identified a number of generic phenomena directly relevant to carbon sequestration including the possibility of leakage through reservoir fissures. This work is an important contribution to a major society problem but also a fundamental contribution to fluid mechanics. In recent work, Vella has developed a theory of delamination of thin films from elastic and liquid substrates, identified new instabilities in capillary and tensional wrinkling, developed new dynamic models coupling surface tension-driven fluid flows to elastic deformation, and suggested new non-invasive methods to measure stress based on elastic instabilities during indentation. In applied mathematics qualities such as originality and creativity are as important as modelling and technical skills, and through his work Vella has already demonstrated that he excels in combining all of these. Vella has made an outstanding contribution to science and mathematics by identifying new and fascinating scientific problems, many of which are technologically relevant, and by combining elegant modelling with in-depth analysis. A Whitehead Prize is awarded jointly to DR DAVID LOEFFLER of the University of Warwick and DR SARAH ZERBES of University College London for their work in number theory, in particular for their discovery of a new Euler system, and for their applications of this to generalisations of the Birch–Swinnerton-Dyer conjecture. Euler systems are at the heart of all progress to date on the Birch–Swinnerton-Dyer conjecture, but progress has been stymied by the difficulty in constructing them. Indeed, only a handful of examples have been found since their introduction in the 1980s, and each of them has led to spectacular progress in number theory (for example, to the recent proof that the Birch–Swinnerton-Dyer conjecture holds for a positive proportion of elliptic curves). Loeffler and Zerbes have constructed a new Euler system, the first to be found in twenty years, and have given remarkable applications of it to Perrin-Riou's $$p$$-adic analogue of the Beilinson conjectures, and to generalisations of the Birch–Swinnerton-Dyer conjecture. In particular they prove new finiteness results for Tate–Shafarevich groups. Their construction uses radically different techniques from previous work, making remarkable use of $$p$$-adic interpolation to prove explicit reciprocity laws. These methods are very flexible and open up the possibility of many more applications in future. APALA MAJUMDAR Anne Bennett Prize 2015 The Anne Bennett Prize is awarded to DR APALA MAJUMDAR of the University of Bath in recognition of her outstanding contributions to the mathematics of liquid crystals and to the liquid crystal community. Apala Majumdar's work on liquid crystal polyhedral confinement tackled the connection between material symmetry and topology in liquid crystals. Using a sophisticated integration of topology and material science, her work on how faceting, corners, edges and geometric singularities interact with material singularities has generated much interest among chemists and material scientists as they develop new encapsulation techniques such as microfluidic devices. Apala Majumdar's work has placed mathematical theory and prediction ahead of actual material physics and is an example of material discovery through mathematics. Her multi-scale work with its mathematically consistent formalism contributes to bridging the gap between molecular and macroscopic formulations, which is of intellectual utility to engineers and device manufacturing. Using geometry and molecular ordering she is able to predict important structures of polyhedral nanoparticles decorated by alkyl chains, and is hence helping to connect molecular modelling and nanotechnology applications. Apala Majumdar has also distinguished herself through her scientific leadership abilities. She has worked with leading research groups around the country in Bristol, Durham and Oxford and internationally in the United States, Europe, Asia and South America; in doing so, she has brought together separate research communities and researchers with diverse scientific backgrounds. The Hirst Prize and Lectureship is awarded jointly to DR JOHN O'CONNOR and PROFESSOR EDMUND ROBERTSON of the University of St Andrews for their creation, development and maintenance of the MacTutor History of Mathematics web site. O'Connor and Robertson created the MacTutor History of Mathematics web site in the early 1990s as enrichment for the Mathematical MacTutor system developed at St Andrews to support the teaching of undergraduate mathematics. By 1995 the web site contained some 1000 biographies of past mathematicians — 200 fuller biographies with portraits and 800 shorter biographies — and about 20 articles on the history of mathematics, and it received some 90,000 hits a month. Since then O'Connor and Robertson have continued to develop and maintain the web site so that it has grown larger, more sophisticated and more reliable. Now it has over 2,800 biographies of mathematicians and related scientists with bibliographies (primary and secondary sources) accompanying each article, around 150 historical articles on mathematical topics, and further resources such as an interactive page on historical curves. The web site has become a hugely successful resource for school children, undergraduates, graduate students and their teachers all over the world, receiving 10,000,000 hits per month during the academic year, with around 2,000,000 distinct users. It is the first port of call for those interested in the historical side of the mathematical sciences, giving mathematicians direct links to their profession's past. It bridges the gap between old books and modern journals, and its biographies give lives to names otherwise known only for the theorems to which they are attached. It is the most widely used and influential web-based resource in history of mathematics. That it has been created and maintained almost exclusively by O'Connor and Robertson is quite remarkable. Edmund Robertson will be invited to give the Hirst Lecture as a part of the prize. CHRISTOPHER BUDD Prize for Communication of Mathematics A Prize for Communication of Mathematics is awarded to PROFESSOR CHRISTOPHER BUDD, OBE, of the University of Bath in recognition of his sustained excellence and innovation in the communication of mathematics. Chris Budd has been vigorously promoting and publicising mathematics and its relevance to everyday practice throughout his career. He has a long track record of initiating, organising, sustaining and leading very effective mathematics communication projects, and of supporting others to become effective communicators of mathematics. The University of Bath's Communicating Mathematics course for undergraduate mathematics students, which Budd initiated in 2003, has now been studied by about 300 students. He is the organiser of Bath Taps into Science, a public science fair with a strong mathematical flavour, and a panel member of the EPSRC Public Understanding of Science Committee. In 2013 he was the mathematics consultant for the London Underground for their 150th anniversary celebrations, designing a mathematics trail for the Underground. Budd is himself a gifted communicator of mathematics. Since 2000 he has been the Royal Institution's Chair of Mathematics, a position through which he has made a substantial contribution to the Royal Institution's Masterclass programme. In 2001 he was the LMS Popular Lecturer, and in 2006 he gave the LMS–Gresham College lecture. He was awarded an OBE in the 2015 Queen's Birthday honours list. He is also an active research mathematician in the fields of scientific computation, dynamical systems, partial differential equations, and mathematical modelling and industrial mathematics, and he combines his research with his work in communication. For example, his Gresham lecture, which showed how clear information can be extracted from fuzzy data, was enriched by his own work on how to distinguish landmine wires from trailing stems in an African jungle. This exemplifies a particular strength of Budd's communications: he has something to communicate because he is an active mathematician. It also makes his contribution to the communication of mathematics especially outstanding. © 2015 London Mathematical Society
TI - Prizewinners 2015
JF - Bulletin of the London Mathematical Society
DO - 10.1112/blms/bdv079
DA - 2015-10-26
UR - https://www.deepdyve.com/lp/oxford-university-press/prizewinners-2015-GlApqMQlPF
SP - 1042
EP - 1055
VL - 47
IS - 6
DP - DeepDyve
ER -