Twisted Sectors in Quasi-Homogeneous Polynomial Singularities and Automorphic Forms
Time: 2022-10-29
Published By: Wenqiong Li
Speaker(s): Jie Zhou (Tsinghua University)
Time: 14:00-15:00 November 8, 2022
Venue: Room 29, Quan Zhai, BICMR
Twisted sectors in singularity theories appear in both Fan-Jarvis-Ruan-Witten theory (Landau-Ginzburg A-model) and Hodge theory (Landau-Ginzburg B-model). In this talk, I will approach them using the language of mixed Hodge structures on the vanishing cohomology. For one-parameter deformations of Calabi-Yau type Fermat polynomial singularities along degree-one directions, we show that twisted sectors in the vanishing cohomology are automorphic forms for certain triangular groups, using the Riemann-Hilbert correspondence. We prove consequently that genus zero Gromov-Witten generating series of the corresponding Fermat Calabi-Yau varieties are components of automorphic forms. If time permits, I will also explain some properties of the so-called Yamaguchi-Yau ring which have shown to be useful in studying higher-genus mirror symmetry.
