The Mathematics of Real and Open Topological Strings

Suny At Stony Brook, Stony Brook NY

Investigators

Abstract

String theory is a model that represents elementary particles by vibrating strings with the aim of unifying the four fundamental forces of nature. While string theory is one of the main paradigms in physics today, it has yet to make experimentally testable predictions. However, it has generated many mathematical predictions that have led to fundamental developments in algebraic geometry and symplectic topology, especially in relation to holomorphic curves. This project's two directions will further test string theory mathematically in the so-called real and open sectors, which have long lagged behind the standard closed sector, and develop the associated mathematical framework and connections between different fields of mathematics, including enumerative algebraic geometry, knot theory, and representation theory. This project will build on work that established the mathematical foundations behind the real sector of string theory, to advance the mathematical understanding of the predictions arising from this sector and to establish the mathematical foundations of the closely related open sector of string theory. The project will also utilize older work that established the BCOV mirror symmetry prediction for counts of genus one curves in a quintic threefold and it will continue the recent work of a current doctoral student that introduced a powerful topological technique for lifting homology relations from Deligne-Mumford moduli spaces of stable curves to moduli spaces of stable (pseudo-) holomorphic maps. 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.