To participate in this seminar, please register HERE.

For any knot in the 3-dimensional space, a singular connection is an SU(2)-connection that is singular along the knot in a controlled way. In particular, holonomy of any such connection along any meridian of the knot is asymptotic to a fixed conjugacy class of SU(2) as the size of the meridian goes to zero. The configuration space of all such singular connections admits a Chern--Simons functional and a circle action. In this talk, I'll give an overview of the construction of a series of knot invariants in the form of 'S-complexes' that are obtained by applying Floer homological methods. I will then discuss some of the structural properties of these knot invariants and some of their topological applications.