Hodge Structures in 8-Dimensional Homotopy Hopf Manifolds

Explore the intricacies of Hodge structures on 8-dimensional homotopy Hopf manifolds in this 56-minute lecture. Delve into ongoing research conducted in collaboration with Dr. Ludmil Katzarkov and Dr. Lino Grama, focusing on manifolds of the form X := Σ^7 × S^1, where Σ^7 represents one of the 28 possible homotopy spheres in dimension 7. Examine the establishment of a map from the moduli space of Hodge structures on H := S^3 × S^1 (the standard 4-dimensional Hopf manifold) to the moduli space of Hodge structures in X. Uncover fascinating connections between X and the K3-surface obtained via topological modular forms (tmf), and consider the potential implications for studying Homological Mirror Symmetry on X through the lens of K3 surfaces.