Seminars & Colloquia Calendar
Monopoles and Fueter sections on three-manifolds
Aleksander Doan - Stony Brook
Location: Hill 705
Date & time: Tuesday, 02 April 2019 at 3:00PM - 4:20PM
Abstract: Over the last thirty years, the study of the Seiberg--Witten equations has led to spectacular advances in low-dimensional topology. In my talk, I will explain a generalization of the Seiberg--Witten equations and its conjectural relationship to Fueter sections, solutions of a non-linear version of the Dirac equation. I will then state some results, obtained in collaboration with Thomas Walpuski, which make progress towards proving this conjectural relationship. While generalized Seiberg--Witten equations are unlikely to lead to new invariants of low-dimensional manifolds, they have an intriguing connection to the geometry of higher-dimensional Riemannian manifolds with special holonomy.