Oct 20 at 17:30 in 507

Title:  Membranes and Maps

Abstract: I will discuss a conjecture relating the equivariant enumeration of maps to a Calabi–Yau fivefold via Gromov–Witten theory and the conjectural M2-brane index. I will explain how this anticipated relation connects the Gromov–Witten theory of fivefolds to the K-theoretic Donaldson–Thomas theory of threefolds and provides a concrete mathematical framework for the refined topological string when the fivefold is a product of a Calabi–Yau threefold with the complex plane. Since a full mathematical construction of the moduli of M2-branes is yet missing the conjectural relation to Gromov–Witten theory can be used to probe its geometry. Using this idea, I will present concrete predictions for a modular interpretation for M2-branes in low curve degree.