Geometry and topology of vector fields in three-dimensions
Speaker: Francesco Lin
Affiliation: Columbia University (USA)
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.
About Maths Colloquium
The Mathematics Colloquium is directed at students and academics working in the fields of pure and applied mathematics, and statistics.
We aim to present expository lectures that appeal to our wide audience.
Information for speakers
Information for speakers
Maths colloquia are usually held on Mondays, from 2pm to 3pm, in various locations at St Lucia.
Presentations are 50 minutes, plus five minutes for questions and discussion.
Available facilities include:
- computer
- data projector
- chalkboard or whiteboard
To avoid technical difficulties on the day, please contact us in advance of your presentation to discuss your requirements.