Unification, Quantum Gravity and Noncommutative Geometry

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A challenging problem in theoretical physics is the unification of the laws of quantum physics with Einstein general theory of relativity. The ideas in this direction that have been pursued most forcefully are superstring theory and noncommutative geometry. These two approaches are intimately related. Noncommutative geometry has provided a new framework to study spaces which could not be handled by the standard methods of Riemannian geometry. It offered a new perspective in the study of gauge theories and the role of the Higgs field and is a promising candidate to describe geometries at Planckian energies. The main focus of this proposal is to study the nature of space-time at sub- Planckian scales and to find its geometric properties and thus determine the dynamics. The broader impact of this research is that the research involves work on the frontiers of noncommutative geometry and will be of benefit to both physicists and mathematicians.