Differential Geometrical Methods in Theoretical Physics

The Impact of Physics on Geometry.- The Impact of Physics on Geometry.- Mathematical Contributions.- Weyl's Program and Modern Physics.- Elliptic Genera of Level N for Complex Manifolds.- The Principle of Triality and A Distinguished Unitary Representation of SO(4,4).- On E 10.- Special Aspects of String Theory.- Operator Methods in String Theory.- On Strings and J.Douglas Variational Principle.- Groupoids and Lie Bigebras in Gauge and String Theories.- Conformal Invariance and Integrable Systems.- The Definition of Conformal Field Theory.- Statistics and Monodromy in Two- and Three-Dimensional Quantum * Field Theory.- Quantum Groups (YBZF Algebras) and Integrable Theories: An Overview.- Integrable Systems and Conformal Invariance.- Algebraic Aspects of Non-Perturbative Quantum Field Theories.- Two Classical Domains: - Symplectic Structures in Physics - General Relativity.- The pairing method and bosonic anomalies.- A Multisymplectic Approach to the KdV Equation.- Singular Points in Level Sets of the Momentum Map and Quantum Theory.- Killing Spinors and Universality of the Hijazi Inequality.- Towards a Renormalizable Theory of Quantum Gravity.- Gauge Theory for Diffeomorphism Groups.- Quantum Field Theory in Curved Spacetime.- Supersymmetric Structures.- Supertheories.- The Integrability Of N = 16 Supergravity.- Conformal Invariant Supersymmetric Theories in Four Dimensions: A Practical Application of BRS Cohomology.- Supermanifolds, Supermanifold Cohomology, and Super Vector Bundles.- Representations of Lie Superalgebras an Introduction.- Concluding Remarks.- Concluding Remarks.- Observations of Two of Our Brightest Stars.- Observations of Two of Our Brightest Stars.