Geometry and Physics of String Compactifications

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Research in string theory in the past three decades has led to exciting new insights in physics and mathematics. Considering string propagation in nontrivial backgrounds produces physical interpretations for mathematical structures in spacetime. The interplay between mathematical and physical intuitions and techniques has enriched both fields. A notable example of this is the discovery and the many applications of mirror symmetry. The research described here will build on these results and on recent progress in both fields to pursue these studies in new regimes. One aim is to improve our understanding of the geometry and physics of heterotic string compactifications using a variety of approaches. These models can describe universes similar to ours with such features as nonabelian gauge symmetry and chiral matter content. In addition an investigation of extremal transitions in M-theory compactifications using insights from geometry and field theory will be carried out to learn about the possible dynamics. This work is expected to lead to a better understanding of the physics of string theory, as well as to insight into the mathematics of CalabiYau spaces. Broader Impact: This work will be done in collaboration with physicists and mathematicians around the world, enhancing interdisciplinary cooperation. Experience shows that such collaborations in this field have been productive , as new physics insights and new results in pure mathematics go hand-in-hand. The PI will also train graduate students and involve undergraduate students in the research. He will also enhance his program of outreach activities. This includes collaborations with local public schools to enhance science teaching and generate enthusiasm for science in young people by visits to the classroom by the PI and/or by students trained by the PI to present specific curriculum materials developed in concert with the schools. These curriculum materials are made broadly available for use elsewhere. The regular public stargazing events conducted by the PI for the past decade will be enhanced by including astrophotography capabilities.