Secondary Fan, Theta Functions, and Moduli of Calabi-Yau Pairs

Explore a comprehensive lecture on the moduli space of Calabi-Yau pairs, focusing on secondary fans, theta functions, and their connections. Delve into a conjecture about the unirationality of connected components in the moduli space of triples involving smooth projective varieties, normal crossing anti-canonical divisors, and ample divisors. Examine the construction of complete toric fans generalizing the Gelfand-Kapranov-Zelevinski secondary fan for reflexive polytopes. Investigate a speculative synthetic construction of the universal family inspired by mirror symmetry, utilizing non-archimedean analytic disk counts. Learn about the construction of the conjectural universal family in the Fano case, generalizing previous work in the toric case. Discover the proof of the full conjecture for del Pezzo surfaces with an anti-canonical cycle of (-1)-curves. Gain insights from speaker Tony Yue Yu of Laboratoire de Mathématiques d'Orsay in this hour-long presentation from the University of Miami.

Secondary Fan, Theta Functions, and Moduli of Calabi-Yau Pairs