| RefNo | EC/1983/43 |
| Previous numbers | Cert XXI, 131 |
| Level | Item |
| Title | Leray, Jean: certificate of election to the Royal Society |
| Date | 1982 |
| Description | Proposal for Foreign Membership. Citation typed on two separate sheets attached to certificate |
| Citation | Original citation
Professor Leray has made fundamental contributions in topology and differential equations which have profoundly influenced the development of mathematics over the past forty years. He introduced the two key notions of sheaves and spectral sequences which have revolutionized modern algebraic geometry and topology. With Schauder in the 1930s he pioneered the uses of topological methods for the treatment of nonlinear problems in analysis. These methods, notably those depending on the seminal concept of Leray-Schauder degree, have been the cornerstones of modern progress in many parts of abstract and applied mathematics. Professor Leray's own work on the theory of the Navier-Stokes equations was crucial to the development of hydrodynamics, and has been the model for many other important developments in applied science. |
Replacement citation
Professor Leray is a mathematician whose work has been of fundamental importance in many areas of pure and applied mathematics. His central interest has always been in the theory of differential equations, and he was in particular a pioneer in the use of topological methods for the analysis of non-linear problems.
His concern with the topology led him to conduct a profound investigation of the way in which a continuous map of topological spaces relates the homology of these spaces. This work (carried out while he was a prisoner of war) introduced simultaneously tow techniques which have become basic to the subsequent development of global methods in topology and geometry. These techniques are the theory of sheaves and spectral sequences.
Sheaf theory deals with the problem of how to pass from a 'local' situation to a 'global' one. It has proved to be a tool of enormous versatility applicable in almost any situation where the distinction of local versus global makes sense. While it has been useful in a purely topological context its most spectacular applications have been in the global theory of several complex variables (as developed by H. Cartan), and in algebraic geometry where J-P. Serre and A. Grothendieck completely revolutionized the subject by a systematic use of sheaf theory.
Spectral sequences are essentially a convenient way of packaging some very complicated algebraic systems that arise frequently in algebraic topology. Since their introduction by Leray they have come to dominate the subject and have proved remarkably effective in a wide range of differential situations. The rapid progress made by algebraic topology in the 1950s and 1960s must certainly be attributed in no small part to the availability of the techniques of spectral sequences.
It is a remarkable fact that Leray, whose primary interest lay in analysis, should have been more influential in geometry and topology than the experts working in these fields.
Leray's early work with Schauder involved generalizing the topological notion of degree to an appropriate infinite-dimensional setting, so that it could be used on spaces of functions. This provided a new and powerful method of proving existence theorems for solutions of non-linear partial differential equations. This Leray-Schauder theory has proved remarkable fruitful and has been at the centre of most subsequent work in the area.
One of the most important sets of differential equations in applied mathematics are the Navier-Stokes equations which govern the motion of fluids. The mathematics of these equations is notoriously difficult and the first significant general results on them were due to Leray. His work has been crucial to the development of hydrodynamics and has been the model for many other important developments in applied science. |
| Extent | 3 sheets |
| AccessStatus | Closed |
Fellows associated with this archive
| Code | PersonName | Dates |
| NA5959 | Leray; Jean (1906 - 1998) | 1906 - 1998 |