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Closed 3-manifolds and modularity

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Campbell Wheeler
Die, 11/10/2022 - 12:15 - 13:45
MPIM Lecture Hall

Contact: Christian Kaiser (

In the early 90s, following some ideas of Witten, quantum invariants were successfully defined for 3-manifolds by Reshetikhin and Turaev. Witten's ideas from physics implied that these invariants should satisfy certain asymptotic properties. This leads to many conjectures such as the volume conjecture. For non-hyperbolic manifolds Lawrence and Zagier showed that the invariants are related to mock modular forms. More recently, the study of hyperbolic manifolds leads to quantum modular forms. I will describe a complete picture in a hyperbolic example, which relates the RTW invariant and new Zhat invariants predicted from physics.



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