The Versatility of Integrability

Columbia University, New York NY

Investigators

Abstract

Ideas and methods of integrable systems played a key role in many celebrated as well as recent advances in algebraic geometry, mathematical physics, probability, and many other areas of pure and applied mathematics. As a particularly striking example one may mention Krichever's recent proof of the famous Welters' conjecture, characterizing Jacobians of algebraic curves among all principally polarized abelian varieties. The conference will bring together experts and young researchers, mathematicians and physicists, people with different backgrounds and different takes on integrable systems, to discuss the latest achievements in this very dynamic field. This conference will be held at at Columbia University in New York, NY, on May 4-7, 2011. A differential equation is called integrable if its solutions may be given by a closed formula, without a recourse to numerical or other approximations. Many highly nontrivial integrable equations were discovered and analyzed both classically and recently. They describe important phenomena in both classical (e.g. certain water waves) and modern theoretical physics and connect to some of the deepest mathematical structures known in pure mathematics. In applied mathematics, they form a basis of perturbative understanding of nearby problems and give a powerful calibration tool for numerical investigations. This conference will bring together the experts working on various aspects of integrability, and will aim to advance our understanding of integrable systems and their applications in algebra, geometry, and physics.