We present a canonical quantization scheme for cylindrically symmetric gravitational waves (Einstein-Rosen waves with two polarizations). It turns out that, in spite of the presence of non-ultralocal terms in the Poisson algebra of currents, the Poisson algebra of transition matrices on the semi-infinite line is correctly defined. Its essentially unique quantization leads to a twisted, centrally extended Yangian double.
Seminar 2: Isomonodromic deformations and theta functions in certain gravity models.
We show how to apply the theory of functions on algebraic curves to solve a certain class of Riemann-Hilbert problems in terms of theta-functions. In turn, this generates theta-functional solutions of associated isomonodromic deformation equations and allows one to calculate the corresponding tau-function.
These results are applied to the gravity models where these Riemann-Hilbert
problems play a central role. In particular, we show how to get a wide class
of solutions of the Ernst equation in terms of theta-functions and simplify
Hitchin's description of self-dual SU(2) invariant Einstein metrics.