PROFESSOR SIR HENRY PETER FRANCIS SWINNERTON-DYER, Bt., KBE FRS, of the University of Cambridge, is awarded the Pólya Prize.
Peter Swinnerton-Dyer has been a world leader in Diophantine number theory for half a century, and his name is associated with some of the deepest unsolved problems in mathematics. He was also a pioneer in practical computer science; computer experimentation played an important part in work on elliptic curves and the Birch–Swinnerton-Dyer conjectures, and served as a precursor of modern computational number theory. His lifelong study of rational points on surfaces has led to a worldwide school of Diophantine geometry, and he continues to lead this field with fascinating and unexpected new discoveries
PROFESSOR MILES REID FRS, of the University of Warwick, is awarded the Senior Berwick Prize for his paper with Alessio Corti and Alexander Puklihkov, “Fano 3-fold hypersurfaces”, published in Explicit birational geometry of 3-folds ( LMS Lecture Notes Series 281). The paper made a big advance in the study of 3-dimensional algebraic varieties. The first deep result on the birational geometry of 3-folds was the 1971 theorem by Iskovskikh and Manin that a smooth quartic 3-fold is not rational. The Corti-Pukhlikov-Reid paper vastly generalizes this result, by showing that all 95 of the Fano hypersurfaces in weighted projective spaces are not rational. In fact, much more is proved: these varieties are “birationally rigid” and in that sense are far from rational. The paper combines the methods of Mori theory with the Russian school of birational geometry, and has formed a foundation for a lot of later work.
PROFESSOR MICHAEL WEISS, of the University of Aberdeen, is awarded the Fröhlich Prize for his use of algebraic topological methods to solve a number of different geometric problems.
His early papers with Andrew Ranicki and Bruce Williams analysed algebraic and homotopy theoretic properties that characterise manifolds amongst topological spaces. He has made important advances in adapting the Goodwillie calculus of homotopy functors to give a new approach to understanding the nature of spaces of embeddings of one manifold in another. In this work he has managed to obtain very specific geometric information by using somewhat elaborate and abstract machinery.
Weiss is most famous for his work with Madsen in resolving a conjecture due to Madsen and Tillmann. They succeed in completely determining the homology type of the moduli spaces of Riemann surfaces as the genus tends to infinity. As a special case they solve Mumford's much studied conjecture about the rational cohomology of this space. It was a surprise that the sophisticated methods of modern homotopy theory together with some well known geometric input would yield these results.
PROFESSOR RAPHAËL ROUQUIER, of the University of Leeds, is awarded a Whitehead Prize for his many incisive contributions to representation theory. The breadth and depth of Rouquier’s work is spectacular. Among some of the topics to which he has made important contributions are: braid groups, Broué’s abelian defect conjecture, stable equivalences of categories of representations, perverse Morita equivalences, representations of Hecke algebras, complex reflection groups, basic sets of Brauer characters, Lusztig families, derived equivalences of blocks of symmetric groups, Cherednik algebras, Deligne-Lusztig varieties, pseudocharacters, and triangulated categories. One of Rouquier’s best known contributions is his recent work with J. Chuang, University of Bristol, showing that the derived category of a block of modular representations of a symmetric group is determined by a single numerical invariant, namely its weight. This result is now a landmark in modular representation theory. The solution of the problem is not only a technical tour-de-force but also uses several techniques previously unfamiliar to workers in the area and points the way forward in a number of directions.
PROFESSOR JONATHAN SHERRATT, of Heriot-Watt University, is awarded a Whitehead Prize for his contribution to mathematical biology and, in particular, the development and analysis of new mathematical models for complex biological processes. He has worked on a broad range of topics. Notable among these are wound healing, pattern formation, tumour growth and spatiotemporal chaos. His work is truly multidisciplinary and often collaborative, and is characterised by originality and novelty. He has published widely in mathematical biology journals and the biological literature. His papers are motivated by biological and medical problems, apply modeling and analysis to understand these, and then provide a significant link back to the biology.
DOCTOR AGATA SMOKTUNOWICZ, of the University of Edinburgh, is awarded a Whitehead Prize for her contributions to noncommutative algebra. In the past six years, Smoktunowicz has solved a number of outstanding problems. She has made the first significant progress for several decades on some fundamental problems concerning nil rings. The most spectacular of these results is the construction, over any countable field, of a simple nil algebra. In a different direction, Smoktunowicz has recently verified the Artin-Stafford Gap Conjecture which is concerned with the possible values of the Gelfand-Kirillov dimension of graded domains; such domains are the setting for the developing theory of noncommutative projective algebraic geometry. In all of her work, Smoktunowicz has introduced novel techniques and constructions and she displays a great ability to deal with long, difficult and technically demanding calculations.
PROFESSOR PAUL SUTCLIFFE, of the University of Kent, is awarded a Whitehead Prize for his many significant contributions to the study of topological solitons and their dynamics. Using a powerful synthesis of analysis, geometry and physical insight, combined with high-intensity computing, he has produced definitive and influential results for a wide range of soliton systems, and has discovered unexpected relations between several of them. In particular, he and his collaborators showed that Skyrme solitons have a polyhedral structure, related to those of carbon fullerenes; and discovered the first stable knotted soliton solution in classical field theory. His recent monograph with Manton is a comprehensive survey of the whole field.
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