Gard Helle will talk in the geometry seminar at 2pm on 04/10/2022. Gard’s title is “Equivariant instanton Floer homology and computations for spherical space forms” and his abstract is below.

*In its most basic form the instanton Floer homology of an integral homology 3-sphere is the homology of a complex freely generated by the gauge equivalence classes of the irreducible flat SU(2)-connections and whose differential is defined via a count of instanton connections over the cylinder associated with the 3-manifold. In 2019 Miller Eismeier introduced a generalization of the above construction that, in particular, defines equivariant instanton Floer groups for rational homology 3-spheres. In this talk I will give an introduction to this equivariant Floer theory and discuss recent and ongoing work concerning computations of these algebraic invariants for the 3-dimensional spherical space forms, that is, the quotient manifolds obtained from the canonical action of a finite subgroup of SO(4) on the 3-sphere.*