Geometry and topology of vector fields in three-dimensions
Francesco Lin, Columbia University
Abstract: Understanding the locus at which a vector field on a manifold vanishes (or more in general k-vector fields are linearly dependent) is a fundamental problem in geometry and topology, dating back at least to the famous Hairy Ball theorem. In this talk, I will discuss some of the history of the problem, with a focus on three dimensions, and discuss a new proof using the Dirac equation of the following theorem of Gromov (and in fact a Riemannian refinement of it): on a closed three-manifold equipped with a volume form, there exist three-vector fields which are volume-preserving and are linearly independent at every point.
Tea and refreshments available from 3:00-3:25 p.m. in the Assmus Conference Room (CU 212).
