Hebrew University topology and geometry seminar

Abstract: In 1970s, a method was developed for integration of nonlinear equations by means of algebraic geometry. Starting from a Lax representation with spectral parameter, the algebro-geometric method allows to solve the system explicitly in terms of Theta functions of Riemann surfaces. However, the explicit formulas obtained in this way are of little or no use for solving such natural topological problems as the problem of Lyapunov stability. The goal of the talk is to demonstrate that these kind of problems can also be approached by means of classical algebraic geometry, and that this approach is very natural and fruitful. In particular, the stability problem for relative equilibria of the free multidimensional rigid body will be considered.