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NCTS Seminar in Algebraic Geometry
 
14:00 - 15:30, May 29, 2020 (Friday)
R440, Astronomy-Mathematics Building, NTU
(台灣大學天文數學館 440室)
Quantum Modularity from 3-Manifolds
Miranda Chih-Ning Cheng (Korteweg-de Vries Institute for Mathematics and Institute of Physics, University of Amsterdam)

Abstract:

Quantum modular forms are functions on rational numbers that have rather mysterious weak modular properties. Mock modular forms and false theta functions are examples of holomorphic functions on the upper-half plane which lead to quantum modular forms. Inspired by the 3d-3d correspondence in string theory, a new topological invariants named homological blocks for (in particular plumbed) three-manifolds have been proposed a few years ago. My talk aims to explain the recent observations on the quantum modular properties of the homological blocks, as well as the relation to logarithmic vertex algebras. The talk will be based on a series of work in collaboration with Sungbong Chun, Boris Feigin, Francesca Ferrari, Sergei Gukov, Sarah Harrison, and Gabriele Sgroi.

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