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On the role of field theories in our physical conception of geometry. Characteristic classes and solutions of gauge theories. Classification of classical yangmills fields. Bundle representations and their applications. to gauge theory. The use of exterior forms in field theory. Electromagnetic fields on Betti numbers, monopoles and strings, minimal coupling. Gravity is the gauge theory of the parallel transport modification of the poincare group. On the lifting of structure groups. On the nonuniqueness of spin structure in superconductivity. Conformal invariance in field theory. Geometric quantization and the WKB approximation. Some properties of halfforms. On some approach to geometric quantization. Representations associated to minimal coadjoint orrits. On the Schrdinger equation given by geometric quantisation. Application of geometric quantization in quantum mechanics. Thermodynamique et Geometrie. Some preliminary remarks on the formal variational calculus of gel'fand and dikii. Reducibility of the symplectic structure of minimal interactions. Ambiguities in canonical transformations of classical systems and the spectra of quantum observables. Quantum field theory in curved spacetimes a general mathematical framework. On functional integrals in curved spacetime. Observables for quantum fields on curved background. Quantization of fields on a curved background. Supergravity. Representations of classical lie superalgebras.
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