Employing D-brane moduli spaces as a unifying theme, this research program consists of three projects lying at the interface between algebraic geometry and string theory. The first is centered around a new mathematical construction (ADHM sheaf invariants) yielding new mathematical conjectures concerning local BPS invariants, quantum cohomologyof quiver varieties and black hole correspondence. The second project investigates the cameral structure and wallcrossing behavior of moduli spaces of Bridgeland stable objects on local surfaces emphasizing a connection between Donaldson-Thomas type invariants and black hole physics. The third proposes a systematic approach to correlators of surface operators in topological gauge theories via virtual cycles and localization for parabolic Higgs bundles. Broader Impact: The interaction between mathematics and string theory has been a major driving force in modern mathematical physics. The research planned here aims at revealing new aspects of this interaction opening new directions of research in Donaldson-Thomas theory, quantum cohomology of quiver varieties as well as fundamental areas of theoretical physics such as black hole physics and string duality. This aims to stimulate the development of several areas of mathematics and physics by unraveling new connections between them. With respect to education, this research program offers multiple training opportunities for students of all levels as well as postdoctoral fellows, stimulating the development of a variety of technical and communication skills with a wide range of applicability beyond the academic environment.
|Effective start/end date||7/15/09 → 6/30/12|
- National Science Foundation (National Science Foundation (NSF))