Charles Doran, University of Alberta
Title: Classification and Applications of K3 Surface Fibered Calabi-Yau Threefolds
Abstract:聽We introduce a generalization of Kodaira鈥檚 theory of elliptic surfaces for threefolds fibered by lattice polarized K3 surfaces. Specializing to fibers of 鈥渘early maximal鈥� Picard rank, we obtain a complete classification (and construction !) for these Calabi-Yau threefolds. The class includes the famous 鈥渜uintic mirror鈥� 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鈥檚 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 鈥渘-sunset鈥� Feynman integrals to all loop orders. This last is joint with Andrey Novoseltsev and Pierre Vanhove.