Extra Seminar - Dr. A. Bolsinov (Loughborough, United Kingdom)

TITLE:             Various faces of integrability: from geometry to algebra and back

ABSTRACT:

The history of integrable systems goes back to 19th century studies in classical mechanics, differential geometry, complex analysis, differential equations and special functions. The theory of integrable systems, in its classical form, studies differential equations which are, in a sense, exactly solvable and possess regular behaviour.

Nowadays, however, integrability is considered in a broader context and is understood as a fundamental phenomenon in mathematics, physics and even more generally, in nature. Due to the links with other areas of mathematics, the theory of integrable systems has become a genuine multidisciplinary area of research and plays a unifying role in mathematics bringing together algebra, geometry and analysis.

In my talk I would like to discuss some aspects of integrability including chaos in integrable geodesic flows, symplectic and topological invariants and new unexpected applications of integrable tops in differential geometry.