
Course
1: O. HIJAZI (France)
Spectral Properties of Dirac Operators and Geometric Structures: Basic
concepts of spin Riemannian Geometry, Dirac Operators and twistors, Weitzenbock
formulas, Gauss formula for spinors, Theorem of Lichnerowicz, spectral
hole, holonomy group.
Course 2: B. BOOSSBAVNBECK (Denmark), S. SCOTT
(U.K.), K. WOJCIECHOWSKI (U.S.A.)
The Determinant of the Dirac Operator: Determinant bundles, Dirac Operators
with boundary conditions and Grassmannians of boundary conditions, Grassmannians
and chiral anomaly, eta invariant, additivity formulas for determinants
and determinant bundles.
Course 3: T. WURZBACHER (France)
Geometric Quantization and twodimensional Quantum Field Theory: Geometric
Quantization and group actions, second fermionic quantization, Geometric
Quantization approach to a fermionic field theory in dimension 2, other
examples of Geometric Quantization in infinite dimension.
Course 4: E. LANGMANN (Sweden)
Representation theory of infinite dimensional groups and algebras
in quantum freld theory: Models in two spacetime dimensions, relation
to anomalies, extensions to higher dimensional quantum field theory models,
presentation of recent results.
