Geometry and Quantum Physics

Notes on Equivariant Localization.- An Introduction to Spin Foam Models of BF Theory and Quantum Gravity.- T-Duality and the Gravitational Description of Gauge Theories.- Noncommutative Geometry and Basic Physics.- An Introduction to Noncommutative Geometry.- Geometric Properties of Transport in Quantum Hall Systems.- q-Deformed Heisenberg Algebras.- Quantum Gravity with Matter Fields in Two Dimensions.- A Quantum Minkowski Space-Time.- Supersymmetry and Nonperturbative Aspects in Quantum Cosmology.- Noncommutative Supergeometry of Graded Matrix Algebras.- Duals for Nonabelian Lattice Gauge Theories.- Absolute Conservation Law for Black Holes.- Double Numbers and Two Dimensional Anomaly Free Field Models.- A Global Path Integral for Yang-Mills Theory.- Anyonic Solutions to the Thirring Model.- Twisting of Quantum Differentials.- Wigner Solid and Laughlin Liquid of Bose Condensed Charge-Vortex Composites.- The Modular Closure of Braided Tensor Categories.- Clifford Algebra as a Useful Language for Geometry and Physics.- Fields on Noncommutative Manifolds.- Geometry of 2-Fold Degenerated 2-Level System.- On q-Deformations and Dunkl-Deformations of Harmonic Oscillators.- Quantum Field Theory in Non-globally Hyperbolic Space-Times.- Steps Beyond the Standard Model in Noncommutative Geometry.- Vacuum Polarization Effects in the Background of Nontrivial Topology.- F-Theory and Toric Geometry.- Actions for Duality-Symmetric Fields.- Unitary Representations of the Quantum Anti-de Sitter Group at Roots of Unity and Elementary Particles.- The Limits of D-Brane Action.