Holomorphic Dynamics

The talk is concerned with regularity of weak solutions of Monge–Ampère equations - fully nonlinear second order partial differential equations.  The main goal is to establish hypoellipticity of weak  solutions and we believe that working in special metric spaces associated with the operator is a promising and powerful approach to  the problem.

Our aim is to study the quantum behaviour of a nearly integrable system in terms of the known Bohr-Sommerfeld spectrum of the original completely integrable system. I shall begin with a discussion of Bohr's quantization rules for the harmonic oscillator. I shall show that a modern interpretation Bohr's quantum conditions together with the Heisnberg's matrix formalism gives rise to a full quantum theory, which naturally leads to an infinite dimensional representation of the Lie algebra of the symplectic group.

I shall begin with a discussion of Bohr’s quantization rules for the harmonic oscillator. I shall show that a modern interpretation Bohr’s quantum conditions together with the Heisnberg’s matrix formalism gives rise to a full quantum theory, which naturally leads to an in…nite dimensional representation of the Lie algebra of the symplectic group.

This will be the second part of Professor P. Zvengrowski's interesting talk on Space Forms.

This talk is an introduction to how integrable systems provide affine models of Riemann surfaces.  As an application, we can compute the Coxeter numbers of some singularities of type A_n.