The Penn Math/Physics group studies a range of topics, all involving significant interactions of ideas from mathematics and physics. For example
* the geometry of metrics with G2 holonomy and their role in M-theory compactifications which are relevant to particle physics; * instantons, vector bundles, and small instanton transitions; * non-Abelian Fourier-Mukai duality; * heterotic M-theory and realistic standard model vacua; * K-theory of gerbes as it relates to both fivebranes and higher boundary topological field theories; * the mathematics of the Ekpyrotic universe and related cosmological scenarios; * notions of stability in triangulated categories as they relate to D-branes;and * black-hole physics via resolution of singularities.
The Penn Math/Physics group studies the rich interdisciplinary boundaries of modern geometry, superstring physics and cosmology. New ideas in algebraic geometry have allowed the formulation of realistic theories of particle physics and quantum gravitation within the context of superstrings and M-theory. Recently, these ideas have led to the concepts of brane worlds, heterotic M-theory and a new formulation of the cosmology of the early universe, Ekpyrotic cosmology. Flowing in the reverse direction, many of the physical concepts in superstring theory motivate new research directions in mathematics, such as the enumerative geometry emerging from mirror symmetry, the new flowering of calibrated geometries, and new results in derived categories, K-theory and gerbes. This award is cofunded by the Programs in Algebra, Number Theory, and Cominatorics, Geometric Analysis, and Topology.
