Table of Contents

Lectures on quantum cosmology.- Solitons and black holes in 4,5 dimensions.- Truncations in Kaluza-Klein theories.- Canonical quantization and cosmic censorship.- Quantum effects in non inertial frames and quantum covariance.- Stochastic de sitter (inflationary) stage in the early universe.- Some mathematical aspects of stochastic quantization.- Superstrings and the unification of forces and particles.- Conformally invariant field theories in two dimensions critical systems and strings.- Liouville model on the lattice.- Exact solvability of semiclassical quantum gravity in two dimensions and liouville theory.- Some features of complete integrability in supersymmetric gauge theories.- Monopoles and-reciprocity.- Non-local conservation laws for non-linear sigma models with fermions.- Inverse scattering transform in angular momentum and applications to non-local effective actions.- General structure and properties of the integrable nonlinear evolution equations in 1+1 and 2+1 dimensions.- Hierarchies of poisson brackets for elements of the scattering matrices.- Multidimensional inverse scattering and nonlinear equations.- An SL(3)-Symmetrical F-Gordon equation:Z?B = 1/3 (eZ?e?2Z).- The solution of the cartan equivalence problem for $$\frac{{d^2 y}}{{dx^2 }} = F(x,y,\frac{{dy}}{{dx}})$$ under the pseudo-group $$\bar x = \varphi (x),\bar y = \psi (x,y)$$ .- Quantum R matrix related to the generalized Toda system: An algebraic approach.- Solution of the multichannel Kondo-problem.- The directed animals and related problems.- Incommensurate structures and breaking of analyticity.