Enumerative Geometry and Modularity in Two-Modulus K3-Fibered Calabi-Yau Threefolds

Explore a mathematical physics seminar that delves into the classification and analysis of smooth M_m-polarized K3-fibered Calabi-Yau threefolds. Learn about their complex structure moduli, focusing specifically on geometries with exactly two moduli, and understand how the choice of generalized functional and homological invariants influences their construction. Discover how variations of Hodge structure are determined by regular periods, expressed through parameters m, i, j, and s. Examine the application of Batyrev-Borisov mirror symmetry in constructing mirror CY 3-folds with two Kaehler moduli, and understand their consistency with the DHT conjecture. Investigate cases where s=0, leading to K3-fibered mirror CY 3-folds with mirror -polarization. Study the derivation of modular expressions for A-model topological string free energies and their connection to Tyurin degeneration of the generalized functional invariant with M_m-polarized K3 central fiber.