The Hairy Ball Theorem (series unlisted)

Abstract: The focus of this talk is representation of Clifford algebra and geometry to show some results for maximum number of independent vector field on n-sphere. I will present a simple proof of the "hairy ball theorem" (exact result for 2-sphere), which says that a ball cannot be continuously covered with hairs that are all flattened that uses ideas from algebraic topology. The talk will then cover spinors which are spin representation of Clifford algebra. Using some basic results in representation theory of Clifford algebras another easy solution will be presented to prove the existence of the above number of independent vector field in n-sphere.

Mathematics

Audience: general audience

Pizza Seminar