Symplektisk geometri, topologisk strängteori och låg-dimensionell topologi
Tidsperiod: 2020-12-01 till 2024-11-30
Projektledare: Tobias Ekholm
Budget: 3 600 000 SEK
Over the last 35 years, the study of the role of geometric and topological aspects of fundamental physics in gauge theory and strings has been a central theme in both theoretical physics and in geometry. New tools and new answers have emerged, but alongside those, new fundamental insights and associated new and deep problems as well. The area is a rapidly developing central part of theoretical science today. The current proposal will further develop aspects of open topological strings and topological M-theory and associated structures in symplectic geometry and low-dimensional topology, by uncovering the underlying geometry.We will in particular study open topological string theory in the light of recent breakthrough results by the applicant and and Shende, where the main idea is to count holomorphic curves with boundary in a Lagrangian 3-manifold of a Calabi-Yau 3-fold by the values of their boundaries in the knot theoretic HOMFLY skein-module. Combined with Symplectic Field Theory, this leads to a mathematically rigorous solution to the three decades old problem of giving an enumerative geometric meaning to the coefficients of the combinatorially defined HOMFLY polynomial of knot theory. This however is just the first application of this viewpoint, the current project will continue and expand this line of research in low-dimensional topology, for Lagrangians and their associated Floer cohomology, and towards a geometric formulation of topological M-theory.