The geometry seminar on 18th May will be given by our very own Andries Salm. The talk will be at 2pm in the Salle des Profs (9th floor of building NO). Andries’s title is “Metric perturbations of degenerate Z/2-harmonic 1-forms” and his abstract is below.
Z/2 harmonic 1-forms are generalizations of harmonic 1-forms that allow topological twisting around a subspace of codimension 2. These objects were introduced by Taubes to compactify the moduli spaces of solutions to generalized Seiberg-Witten equations, and they show up in many other gauge theoretical problems.
Donaldson showed there is a deformation theory for so-called non-degenerate Z/2-harmonic 1-forms. In this presentation metric we study the perturbations of the remaining degenerate solutions. For a natural class of degenerate examples, we prove that after a suitable perturbation of the ambient Riemannian metric, the form can be deformed to a nearby non-degenerate Z/2-harmonic 1-form.