Classification and Applications of K3 Surface Fibered Calabi-Yau Threefolds

Charles Doran
(University of Alberta)
Seminar
Wednesday, 10 October, 2018, at 16:15-17:15, in Aud. D2 (1531-119)
Abstract:
We introduce a generalization of Kodaira’s theory of elliptic surfaces for threefolds fibered by lattice polarized K3 surfaces. Specializing to fibers of “nearly maximal” Picard rank, we obtain a complete classification (and construction!) for these Calabi-Yau threefolds. The class includes the famous “quintic mirror” and its Hodge-theoretic analogues. This is joint work with Andrew Harder, Andrey Novoseltsev, and Alan Thompson. Time permitting, we will formulate two applications in theoretical physics. The first, already mentioned in yesterday’s Colloquium, is to my new mirror symmetry conjecture with Harder and Thompson. The second uses the periods of an iterated fibration structure in a tower of Calabi-Yau manifolds to recursively construct the “n-sunset” Feynman integrals to all loop orders. This last is joint with Andrey Novoseltsev and Pierre Vanhove.
Organised by: QGM
Contact person: Artan Sheshmani