# MSCA Fellow choose QM

Prestigious Marie Skłodowska-Curie Individual Fellowship is awarded to a postdoc with Centre for Quantum Mathematics as host institution.

One of the prestigious two-year Marie Skłodowska-Curie Fellowships is awarded to Dr. Nezhla Aghaei with QM Centre Director Jørgen Ellegaard Andersen as supervisor.

Nezhla Aghaei comes from a postdoc position at the Max Planck Institute of Mathematics in Bonn and obtained her PhD in 2016 from DESY and University of Hamburg under the supervision of Jörg Teschner.

Her MSCA project is called: “Super Andersen-Kashaev Topological Quantum Field Theory”. A topological quantum field theory (TQFT) is a model of quantum field theory which computes topological invariants. Although TQFTs were invented by physicists, they are also of mathematical interest because of their relation to quantum topology. Particularly interesting examples of 3d TQFTs arise from Chern-Simons (CS) theory with non-compact gauge groups.

A connected component of the phase space of PSL(2,R) CS theory is identified with Teichmüller space, and its quantum theory corresponds to a specific class of unitary mapping class group representations in infinite dimensional Hilbert spaces. By using quantum Teichmüller Theory (qTT), Andersen and Kashaev construct a one parameter family of TQFT's defined on certain shaped triangulated pseudo 3-manifolds.

On the other hand, Teichmüller theory has an interesting generalization originating from the deformation theory of super Riemann surfaces which initially was motivated by super string perturbation theory. In the super generalized case, the gauge groups is replaced by the super group OSP(1|2). QTT of super Riemann surfaces has been constructed by using coordinates associated to the ideal triangulations of super Riemann surfaces.

To this date, we lack mathematical understanding of TQFT's with non-compact super gauge groups. This proposal aims to construct and study TQFT's based on super qTT as follows: Construction of the tetrahedral partition functions from the mapping class groupiod representations of super qTT using a version of charging, establish tetrahedral symmetries and prove well-definedness and topological invariance for a certain class of triangulated shaped pseudo 3-manifolds and finally make calculations for different examples.

These results are expected to build a bridge between very different areas of mathematics, thus possibly opening new research gates completely inspired by physics.

##### The MSCA Fellow

Dr. Nezhla Aghaei