Did you know that at any given point of time, there is a location on Earth where the wind speed is zero? The reason lies in the theory of vector fields. Vector fields are easily observable in nature and are widely used in sciences like physics or climate science. In mathematics, vector fields are part of the deep and powerful theory of vector bundles. In this talk, I’ll start off with a basic introduction to vector bundles and we’ll look at some simple examples. We'll try to understand why vector bundles are so useful and their relation to other areas of mathematics. In the end we’ll discuss the “Hairy Ball Theorem” and some consequences of it. I will develop most of the concepts required during the talk but some familiarity with basic topology will definitely be useful.

Resources: -

Slides of the Talk