The Polya Prize is awarded to Professor N.J. Hitchin FRS of Oxford University for his fundamental and enormously influential contributions to geometry, as well as for his wider contributions to the development of mathematics and mathematical physics.
Nigel Hitchin is one of the world's foremost geometers, and beyond that he has exercised a major influence on the shape of theoretical physics. For over 20 years Nigel Hitchin has been producing a remarkable succession of highly original and influential papers in differential geometry. The range of topics is extensive: minimal surfaces, integrable systems, moduli spaces, symplectic and Kähler geometry, Einstein metrics, hyper-Kähler manifolds. He has used a broad range of techniques, many involving novel interactions with complex algebraic geometry, and has produced definitive results.
One masterpiece is his work on the self-duality equations and his identification of the "Hitchin moduli space" of holomorphic bundles equipped with a Higgs field. This has provided the basis for many developments in the theory of integrable systems. The space has been central in recent years in the work of Beilinson and Drinfeld on Langlands duality in representation theory. In mathematical physics, Hitchin's work on monopoles and spectral curves have been essential to implementing Manton's ideas about slow-motion scattering. His research continues at full pace.
Hitchin was President of the Society from 1994 to 1996. He has, with quiet efficiency, played a significant role in ensuring the healthy development of mathematics in this country and abroad.
The Naylor Prize is awarded to Professor M. H. A. Davis of Imperial College, who has made excellent pioneering contributions to stochastic analysis, stochastic control and filtering theory and more recently to mathematical finance. His expository work is of enormous influence in introducing modern mathematical methods into these areas.
In his earliest work, Mark Davis gave a rigorous foundation for stochastic optimal control, and was the first to introduce martingale techniques into stochastic control; these techniques were central to subsequent developments and extremely novel at the time.
Mark Davis contributed to the theory of robust non-linear filtering, giving a representation of the nonlinear filter in a form which is uniformly continuous in terms of the observation. This result is important in theory and in practice. He derived a separation principle showing that the optimal control problem can be decomposed into the optimal filtering of the observations together with a suitably designed control.
Professor Davis introduced the notion of piecewise-deterministic Markov processes and developed the stochastic calculus and the optimal control theory for such processes. These results are useful in inventory control and queuing systems.
In his position as Director of the Research Unit of a leading international investment bank, Davis became one of the most respected and authoritative figures applying stochastic analysis to mathematical finance, fashioning the mathematical tools finance uses.
Professor Davis is a distinguished scientist who has worked on problems of wide applicability, and made fundamental contributions which he has elegantly conveyed in lectures, articles and books.
The Senior Berwick Prize is awarded to Professor Jeremy Rickard of Bristol University, for his two papers:
1. Idempotent modules in the stable category, JLMS 56(1997),149-170;
2. Splendid equivalences: derived categories and permutation modules, PLMS 72(1996),331-358.
Paper 1 develops a fruitful analogue, in the stable module category of a finite group, of a basic localization technique in algebraic topology, and has led to progress on the structure of stable module categories. Paper 2 relates to famous conjectures of Broué on equivalence of categories for derived categories for block algebras of finite groups, and has proved fundamental for the theory of blocks with abelian defect groups.
A Whitehead Prize is awarded to Dr K.M. Buzzard of Imperial College for his distinguished work in number theory.
Dr Buzzard has several main achievements:
(i) he has given a basically complete description of the possible levels for a modular mod l Galois representation;
(ii) he has given a Galois-theoretic criterion for analytically continuing a p-adic modular form to a classical modular form;
(iii) he has shown that the Coleman-Mazur theory of p-adic families of modular forms could be de-mystified by short elementary arguments using group cohomology; and
(iv) he has shown how to compute the slopes of the p-Hecke operator on spaces of modular forms.
A Whitehead Prize is awarded to Dr Alessio Corti of Cambridge University for his fundamental contributions to the geometry of 3-folds. He has carried on Mori's famous method of minimal models, and refined it to allow classification of varieties which are roughly similar to projective space. Building on previous work on Fano varieties by the Russian school of Iskovskikh and Manin, Corti introduced techniques and a conceptual framework for systematic study of the notion of birational rigidity. He is internationally recognised as having made major contributions to the Sarkisov program, and to the classification program for Fano varieties. His influential foreword, jointly with Miles Reid, to the London Mathematical Society Lecture Notes on Explicit birational geometry of 3-folds outlines the subject of explicit birational geometry, going from the abstract notions of the Mori program towards tractable lists of terminal singularities, divisorial contractions, flips, Fano 3-folds and the like. He is distinguished both for his technical contributions to fundamental classifications, and for his vision of the most illuminating methods for further progress.
A Whitehead prize is awarded to Dr Marianna Csörnyei of University College London who has produced important and impressive results in a wide range of directions, from real analysis to geometric measure theory, to geometric nonlinear functional analysis. Among these, both for significance and originality, one could cite her work on the equivalence of different notions of null sets in infinite dimensional spaces, the construction of a Lipschitz quotient between space of different - finite - dimensions which does not satisfy Gorelik's principle, and a remarkable proof that given a locally-finite measure on the plane, every set in the plane can be covered by a union of lines with the same measure, a far-reaching extension of a result of R.O. Davies.
A Whitehead prize has been awarded to Constantin Teleman of Cambridge University, who has made important contributions to the representation theory of infinite dimensional groups, especially loop groups. His work has used a wide variety of techniques from analysis, algebra and topology and has led to the resolution of several much studied conjectures.
He discovered a powerful analogue of the Borel-Weil-Bott theorem valid for loop groups, thus taking an important further step in the development of the representation theory of loop groups. This fundamental result has many consequences including a beautiful treatment of the Verlinde conjecture about loop group representations and the solution of a conjecture of Bott that holomorphic induction takes tensor products to fusion products.
His work on geometric quantisation implies a strong version of the ‘quantisation commutes with reduction’ conjecture of V. Guillemin and S. Sternberg.
In joint papers with S. Fishel and I. Grojnowski he has studied the cohomology of the Lie algebra of vector fields on C which vanish to high order at a point. A consequence is a proof of the ``strong Macdonald conjectures''.Very recently, together with D. Freed and M. Hopkins, Teleman has given a very surprising description of the Verlinde representation ring of the loop group of a compact group G in terms of the twisted equivariant K-theory of G.
Teleman has uncovered surprising connections between mathematical objects previously not known to be related and has found elegant proofs of a number of outstanding conjectures.
| Back to top LMS Site Contents Home |
Editorial Control:
J.T. Stuart webmaster@lms.ac.uk Last changed: 11.02.02 |