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Invariant Theory with Applications
| Credits | 8 credit points |
| Instructors | Draisma, J. (Technische Universiteit Eindhoven), Frenk, B.J. (Technische Universiteit Eindhoven), Gijswijt, D.C. (Universiteit Leiden), Gijswijt, D.C. (CWI) |
| jdraisma@win.tue.nl, b.j.frenk@tue.nl, dion.gijswijt@gmail.com, dion.gijswijt@gmail.com | |
| Aim | Invariant theory is a classical subject in mathematics, which recently has found exciting new applications in combinatorics and (algebraic) statistics. This course is an efficient introduction into invariant theory, culminating in the treatment of some of these new applications. |
| Description | -Basics: multilinear algebra, group actions, representations, equivariant maps, Schur's lemma. -Symmetric functions, characterisation of polynomials having only real roots. -Hilbert's finiteness theorems for reductive group actions -Applications coding theory -Linear reductiveness of classical groups -properties of quotient maps and null cones -Polarisation and restitution -Weyl's First Fundamental Theorems -Degree bounds on invariant rings -Applications to phylogenetic tree models -Applications to graph invariants |
| Organization | Each class there will be three 45 minutes time slots: two lectures and one exercise class. |
| Examination | The final grade will be based exclusively on weekly homework. |
| Literature | (very) concise lecture notes will be handed out during the course. Collateral reading will appear on the course website |
| Prerequisites | linear algebra, groups, rings, fields. |
| Remarks | Invariant Theory with Applications will not be held on November 10th, 2009 |