Special Lecture "Modularity of Calabi-Yau Manifolds" by Prof. Noriko Yui (Queen’s University)

Special Lecture

• Noriko Yui - Professor, Department of Mathematics and Statistics, Queen’s University
• Date: Friday, February 22
• Time: 10:00-16:00
• Venue: Lecture Room B715, Lab3

Modularity of Calabi-Yau Manifolds

Abstract: Let X be a Calabi-Yau manifold of dimension d. In this talk, I would like to address the modularity questions around Calabi-Yau manifolds. We will confine ourselves to Calabi-Yau manifolds of small dimensions, e.g., d ≤ 3. There are two types of modularity:

(A) Arithmetic modularity/automorphy. This is concerned with Calabi-Yau varieties defined over Q (or number fields). The main questions are the modularity/automorphy of the cohomological L-series of the l-adic Galois representations associated to these varieties in the framework of Langlands Philosophy.

(G) Geometric modularity. This is concerned with families of Calabi-Yau manifolds. The main questions are the modular/automorphic properties of various invariants associated to these varieties, e.g., mirror maps, Gromov-Witten invariants, Donaldson-Thomas invariants, holomorphic anomaly equations, etc. arising in string theory. Quasi-modular forms, Jacobi forms, Siegel modular forms,  and more general modular-like  forms show their appearances in this landscpae.