M-Theory and Quantum Geometry

1 D Branes in String Theory, I.- 1 Introduction.- 2 Perturbative String Theory.- 3 Conformal Field Theory Formulation.- 4 T-Duality.- 5 Classical Solutions of The Low-Energy String Effective Action.- 6 Bosonic Boundary State.- 7 Fermionic Boundary State.- 8 Classical Solutions From Boundary State.- 9 Interaction Between a p and a p’ Brane.- 2 Moduli Spaces of Calabi-Yau Compactifications.- 1 Introduction.- 2 A short story about string theory, F-theory and M-theory.- 3 The q = 16 triplet.- 4 The q = 8 triplets.- A Calabi-Yau manifolds.- 3 The M(Atrix) Model of M-Theory.- 1 Introduction.- 2 Matrix theory from the quantized supermembrane.- 3 The BFSS conjecture.- 4 M-theory objects from matrix theory.- 5 Interactions in matrix theory.- 6 Matrix theory in a general background.- 7 Outlook.- 4 The Holographic Principle.- 1 Black Hole Complementarity.- 2 Entropy Bounds.- 3 The AdS/CFT Correspondence and the Holographic Principle.- 4 The Flat Space Limit.- 5 Born-Infeld Actions and D-Brane Physics.- 1 D-Brane Solitons and the Born-Infeld Action.- 2 Born-Infeld Dynamics of Branes in Flat Space.- 3 Branes in Curved Space and the Gauge Theory Connection.- 4 Born-Infeld Analysis of the Baryon Vertex.- 5 Applications of the AdS/CFT Correspondence.- 6 Summary.- 6 Lectures on Superconformal Quantum Mechanics and Multi-Black Hole Moduli Spaces.- 1 Introduction.- 2 A Simple Example of Conformal Quantum Mechanics.- 3 Conformally Invariant N-Particle Quantum Mechanics.- 4 Superconformal Quantum Mechanics.- 5 The Quantum Mechanics of a Test Particle in a Reissner-Nordström Background.- 6 Quantum Mechanics on the Black Hole Moduli Space.- 7 Discussion.- A Differential Geometry with Torsion.- 7 Large-N Gauge Theories.- 1 Introduction.- 2 0(N) Vector Models.- 3 Large-N QCD.- 4 QCD in LoopSpace.- 5 Large-N Reduction.- 8 Introduction to Random Surfaces.- 1 Introduction.- 2 Random paths.- 3 Branched polymers.- 4 Dynamicaly triangulated surfaces.- 5 Lattice surfaces.- 6 Conclusion.- 9 Lorentzian and Euclidean Quantum Gravity ¡ª Analytical and Numerical Results.- 1 Introduction.- 2 Lorentzian gravity in 2d.- 3 Topology changes and Euclidean quantum gravity.- 4 Euclidean quantum gravity.- 5 Numerical setup.- 6 Dynamically triangulated quantum gravity in d > 2.- 7 Outlook.