The next department seminar will be at the usual place**, but it starts*** half an hour later than usual, at 2.30pm*.

Abstract: By the well-known "hedgehog theorem", every (tangential)

vector field on the sphere S^2 must vanish somewhere. More generally,

Poincaré proved that one can find a nowhere zero vector field on the

n-dimensional sphere S^n if and only if n is odd. This result raised

the question how many pointwise linearly independent vector fields can

be found on S^n for a given n. The solution of this problem consists

of two parts. First, we have to construct as many linearly independent

vector fields on S^n as we can, then it has to be proved that the

maximal number is reached. In this lecture we focus on the first part

and show how representation theory of Clifford algebras tells us the

maximal number of pointwise linearly independent linear vector fields

on S^n. This number cannot be exceeded even if we drop the linearity

condition on the vector fields, by a theorem of Adams.

You can watch the lecture here:

https://www.youtube.com/watch?v=9nRU8OKKZN0&index=1&list=PL_0phSnA7tyQJD...