Quantum Groups and Related Topics

Part 1 Quantum groups: Sugawara construction and the Q-deformation of Virasoro algebra; complex quantum groups and their dual Hopf algebras; external projector and universal R-matrix for quantized contragredient lie (super)algebras; quantum deformations of D=4 Poincare algebra; "Quantum Group" strecture and "Covariant" differential calculus on symmetric algebras corresponding to commutation factors on Zn; remarks on the use of R-matrices; construction of some Hopf algebras; realifications of complex quantum groups. Part 2 Non commutative differential geometry: on multigraded differential calculus; Yang Mills fields and symmetry breaking - from lie super-algebras to non commutative geometry; differential and integral calculus on the quantum C-plane. Part 3 Integrable systems: rigorous approach to Abelian Chern-simons theory; the conformal block structure of perturbation theory in two dimensions; an alternative dynamical description of quantum systems; on the solutions of the Yang-Baxter equations; state sum invariants of compact 3-manifolds with boundary and 6j-symbols. Part 4 Miscellaneous: product of states; quantum measurements and information theory; a comment on a 3-dimensional euclidean supersymmetry; chiral nets and modular methods; chiral symmetry breaking-rigorous results; on a twister shift in particle and string dynamics; the metric of bures and the geometric phase.