Polopoly will be shut down December 15, 2023. Existing pages will have to be moved or removed before that date. Empolyees may read more at FAQ Polopoly Avveckling

MAI0086
Geometric multilinear analysis

Number of credits: 8 hp

Examiner: Andreas Axelsson

Course literature: A. Axelsson: "Geometric multilinear analysis" (compendium).

Course contents:
- Basic geometric algebra in affine and inner product spaces: exterior, Clifford, quaternion algebra.
- Plücker's equations and the Grassman cone, Clifford and spin groups.
- Isometries and conformal maps in euclidean and Minkowski spaces: Vahlen/Ahlfors matrices, Liouville's theorem on higher dimensional conformal maps.
- Representation of Clifford algebras.
- Exterior and interior differentiation, pullbacks and pushforwards.
- Vector valued integration on k-surfaces in affine spaces, Stokes' theorem.
- Hypercomplex analysis: Hodge--Dirac operator, Clifford--Cauchy integrals, spherical harmonic and monogenic functions.
- Poincaré's theorem, Hodge decompositions on bounded domains with Lipschitz boundary, and some cohomology theory.

Organisation: Lectures.

Examination: Hand-in assignments and oral presentations.

Prerequisites: Linear algebra, Vector calculus, Several variables calculus, Complex analysis, Abstract algebra.

Page manager: karin.johansson@liu.se
Last updated: 2014-04-29