# MS Seminar (Mathematics - String Theory)

Speaker: Ioana-Alexandra Coman (Amsterdam) Quantum modularity of higher rank homological blocks Thu, Dec 02, 2021, 17:00 - 18:30 Zoom 2750.pdf 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 BPS spectra for certain 3d $\mathcal{N}=2$ theories $T[M_3]$. At the same time, these SQFTs are associated to 3-manifolds $M_3$ by a compactification of the 6d $\mathcal{N}=(2,0)$ SCFT which lives on a stack of M5 branes, with $M_3$ at the internal space. The $\hat{Z}$ invariants have been related to other topological invariants, and they have been furthermore shown to possess interesting number-theoretic features. They have been proven to be quantum modular forms in cases where $T[M_3]$ has gauge group $SU(2)$. After reviewing these developments, here I explore certain higher rank extensions and emerging features of the corresponding $\hat{Z}$ invariants.