Date and Time : 28th July 2021, 21:00 JST
Speaker : Ioana Coman (University of Amsterdam)
Title : Quantum modularity of 3-manifold invariants and higher depth extensions
Abstract :
A recently proposed class of topological 3-manifold invariants $\hat{Z}[M_3]$ which admit series expansions with integer coefficients has been the focal point of intense research over the past few years. Their definition has its origins in the computation of the BPS spectrum of the 3d $\mathcal{N}=2$ theory $T[M_3]$ which is associated to $M_3$ by the compactification on this 3-manifold of the 6d $\mathcal{N}=(2,0)$ SCFT living on a stack of $N$ M5 branes and, under the 3d-3d correspondence, the $\hat{Z}$-invariants are therefore related to the WRT invariant of $M_3$. Subsequently, $\hat{Z}[M_3]$ have also been shown to possess interesting number-theoretic features, proving themselves to be quantum modular forms in the case where $T[M_3]$ has gauge group $SU(2)$. After reviewing these developments, here we explore certain extensions to higher rank cases and features of the corresponding $\hat{Z}$ invariants.
Location : Zoom Announcement on Research Seminars
Ancilliary Material :
Slides
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