Posted on 18 January 2017
Professor Sklyanin is one of the leading experts on the phenomenon of integrability, and is renowned for his key contributions to the modern theory of integrable systems.
Integrable systems attract enormous interest from mathematics and physicists. Integrability is a very rare situation in mechanics, and describes the situation where motion can be defined by a single, simple, formula. An example of an integrable system is that of the Earth travelling around the Sun in an elliptic orbit according to the extremely simple formulae derived by Kepler and Newton. The integrability, however, is a fragile property: adding a third body, like the Sun-Earth- Moon interaction, makes the system chaotic. While in the 19th Century, the list of known integrable systems would only have filled half a page, a breakthrough in the 1960s (called the ‘Inverse Scattering Method’) precipitated the discovery of many of new integrable systems. These newly found systems included waves on water, the behaviour of superconductors and even elementary particles. Integrability was found not only in classical mechanics but also in quantum and relativistic mechanics.
Professor Sklyanin's new project links integrability to hypergeometric analysis, which involves functions more complicated than the elementary functions, sine, exponential, or logarithm etc. Hypergeometric analysis has a long and glorious history, involving great mathematicians including Gauss, Euler and Weierstrass. The aim of this project is to study the use of hypergeometric functions to solve quantum integrable systems. Professor Sklyanin said “I am very pleased to receive the Fellowship and to be able to concentrate on my research. The theory of integrable systems is a very synthetic discipline, tying together multiple branches of mathematics and physics. I believe that the results of the outlined program will be of interest not only for the integrable community in the UK and worldwide but also have a wider impact on mathematics and physics where hypergeometric functions are known the play an important role”.
Professor Sklyanin joined the Department of Mathematics in 2001, and was elected Fellow of the Royal Society in 2008.