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SUMMARY:Mock modular forms as Z-invariants - Ioana Coman (University of To
 kyo)
DTSTART:20231002T133000Z
DTEND:20231002T143000Z
UID:TALK200818@talks.cam.ac.uk
DESCRIPTION:A new family of topological 3-manifold invariants&nbsp\;has be
 en proposed recently\,&nbsp\;with the property that they are q-series with
  integrality properties that allow categorification. They have a mathemati
 cal definition based on the data which specifies the associated 3-manifold
 \, though this is of&nbsp\;limited&nbsp\;applicability and&nbsp\;restricte
 d&nbsp\;to cases which satisfy a certain negativity condition. Aside from 
 their relevance in topology\, these invariants have proven to be of&nbsp\;
 broad&nbsp\;interest through&nbsp\;a web of relations.&nbsp\;Physically\,&
 nbsp\;they capture the&nbsp\;partition functions of certain 3-dimensional 
 SQFTs\, while&nbsp\;from a&nbsp\;number theory&nbsp\;perspective&nbsp\;the
 y provide examples of holomorphic quantum modular forms.&nbsp\;Here I will
  discuss an underlying hidden symmetry of these invariants and how&nbsp\;c
 onsiderations of modularity can be leveraged to&nbsp\;predict&nbsp\;what t
 hese should be for manifolds&nbsp\;not covered by their original definitio
 n\, as well as the wider implications of these results.&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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