ERC Starting Grant · 2021
Correspondences in enumerative geometry: Hilbert schemes, K3 surfaces and modular forms
Enumerative geometry is concerned with counting geometric objects on spaces defined by polynomial equations. The subject, which has roots going back to the ancient Greeks, was revolutionized by string theory in the 90s and has since become a fundamental link between algebraic geometry, representation theory, number theory and physics. With K3Mod I propose to establish a wide range of new correspondences in enumerative geometry. These link together different enumerative theories and open new perspectives to attack long-standing problems concerning the quantum cohomology of the Hilbert scheme of points on surfaces, modular properties of invariants of K3 surfaces, string partition functions of…
From the public funding record at EU CORDIS. Describes the funded project, not the reviews below.