Our very own Andries Salm will speak in the differential geometry seminar on Monday 21st October. The talk will take place at 2pm in the Salle des Profs (9th floor of building NO, Campus de la Plaine). Andries’ title is *“Construction of Z_2 harmonic 1-forms on closed 3-manifolds with long cylindrical necks”* 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, called the singular set. These objects were introduced by Taubes to compactify the moduli spaces of solutions to generalized Seiberg-Witten equations, but they show up in many other gauge theoretical problems. Although their usefulness, very little is known about them. Even worse, for a generic metric, no Z_2 harmonic 1-forms exists.*

*In this presentation we will revisit the reason behind their scarcity and how it relates to an infinite dimensional obstruction space. We show how under suitable deformations this can be simplified to a topological condition, which enables us to construct a Z_2 harmonic 1-forms for every smooth singular set.*