Real Gromov-Witten Theory and its Applications

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 (pseudo-)holomorphic curves. This project’s two directions will further test string theory mathematically, aiming to verify its predictions for the behavior of holomorphic curves in various settings and to investigate the expected connections between different fields of mathematics, including enumerative algebraic geometry, knot theory, and representation theory. This award will also support the PI's graduate students. This project will build on the PI’s previous work, which established the mathematical foundations behind the real sector of string theory, to advance the mathematical understanding of the so-called mirror symmetry predictions arising from this sector. It will also utilize the PI’s decade-old work, which established the BCOV mirror symmetry prediction for counts of genus 1 curves in the renown quintic threefold and continue the recently completed work on the topology of Deligne-Mumford moduli spaces of stable real curves with conjugate pairs of marked points. 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.