Quantum gravity conjectures and asymptotic Hodge theory

In the first part of the talk I will motivate why asymptotic Hodge theory is useful to study quantum gravity conjectures within string theory. In particular, I will briefly discuss the distance conjecture and the claim that certain integral classes, known as self-dual background fluxes, are finite. In the second part, I will explain some recent results that arose from this application. In particular, I will show how the matching of sl(2) boundary data to nilpotent orbits and associated lifted period mappings can be carried out systematically for Calabi-Yau threefolds and fourfolds. Starting with the classification of possible sl(2) boundary structures, I will use the sl(2)-orbit theorem to recover some well-known period vectors for Calabi-Yau manifolds with few moduli. I will suggest interpreting this as a holographic correspondence for the moduli space. Zoom notes: Meeting ID: 972 6526 6011