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.

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Last updated: 2014-04-29