Title：[NTU-NCTS String Seminar] Reversing the orientation: new frameworks for the computation of Z-hat invariants for positive Seifert manifolds 
Speaker：Davide Passaro (Amsterdam U.) 
Time: Oct. 27, 2023 (Fri.) 14:30-15:30
Venue: Rm. 815, Dept. of Physics, NTU

Abstract: 
Z-hat invariants are topological invariants for three manifolds that have
deep physical meaning and are intimately related to Cern-Simons theory.
Current computational methods only allow for the computation of Z-hat invariants
only on a subset of Seifert manifolds which satisfy a negativity property.
On such manifolds the Z-hat invariant are Quantum Modular Forms. CP symmetry
on Chern-Simons theory suggests a relation between Z-hat invariant on pairs
of negative and positive Seifert manifolds related by orientation reversal.
A direct application of the Chern-Simons relation on known Z-hat however
leads to diverging series. By leveraging the quantum modularity of the
Z-hat invariant however it is possible to understand the Chern-Simons relation,
and additionaly to predict the specific quantum modular properties of the proposed
Z-hat invariant on positive Seifert manifolds. This prediction is known as the
False-Mock conjecture. We find that, in specific cases where we can either regularize
the diverging series or we can re-express the Z-hat invariant using inverted Habiro
series that the relation can be applied the False-Mock conjecture is satisfied.