Algebraic Geometry and Strings

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Exploration of the interactions of physical theories (string theory and quantum field theory) with mathematics (especially algebraic geometry) has been extremely productive for decades, and the power of this combination of tools and approaches only seems to strengthen with time. The goal of this project is to explore and push forward some of the major issues at the interface of algebraic geometry with string theory and quantum field theory. The research will employ and combine a variety of techniques from algebraic geometry, topology, integrable systems, String theory, and Quantum Field theory. The project also includes many broader impact activities such as steering and organization of conferences and schools, membership of international boards and prize committees, revising Penn’s graduate program, curricular development at the graduate and undergraduate level, advising postdocs, graduate and undergraduate students, editing several public service volumes and editing of journals and proceedings volumes.More specifically, the project includes, among other topics: a QFT-inspired attack on the geometric Langlands conjecture via non-abelian Hodge theory; a mathematical investigation of physical Theories of class S in terms of variations of Hitchin systems; applications of ideas from supergeometry to higher loop calculations in string theory; exploration of moduli questions in algebraic geometry, some of them motivated by a QFT conjecture, others purely within algebraic geometry; further exploration of aspects of F theory and establishment of its mathematical foundations; and exploration of categorical symmetries and defect symmetry TFTs. Each of these specific research areas represents a major open problem in math and/or in physics, whose solution will make a major contribution to the field.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.