Abstract

Three Physics Visions.- Notes on and Noncommutative Geometry.- Quantum Gravity as Sum over Spacetimes.- Lectures on Quantization of Gauge Systems.- Novel Mathematical Tools.- Mathematical Tools for Calculation of the Effective Action Effective Action in Quantum Gravity.- Lectures on Cohomology, T-Duality, and Generalized Geometry.- Stochastic Geometry and Quantum Gravity: Some Rigorous Results.- Afterthoughts.- Steps Towards Quantum Gravity and the Practice of Science: Will the Merger of Mathematics and Physics Work?.

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