3-dimensional Seiberg--Witten theory and mirror symmetry

The 4-dimensional Seiberg--Witten invariants provide interesting numbers allowing one to study smooth structures on 4-manifolds. They possess the structure resembling that of a topological quantum field theory where to a 3-manifold one associates the monopole Floer homology and to a 4-manifold the Seiberg--Witten invariants. The goal of this project is to
define a fully extended 3-dimensional TQFT underlying simplified, 3-dimensional, Seiberg--Witten invariants. A guiding tool will be provided by the theory of 3-dimensional mirror symmetry relating them to the Rozansky--Witten invariants.