Physics 500-006, Fall, 2005
A Seminar in Group Theory, with extra advanced topics
Original Syllabus
| Fall 2005 | Wednesday, 11:00 - 12:00 Noon, in Room 190 | Daniel Finley | |
| Lie Groups & Lie Algebras: perhaps 6-8 weeks | mostly by Finley | ||
| Lie Algebras: |
Contragredient Algebras, Cartan matrices, local parts, graded algebras,
root lattices, Serre conditions, Dynkin diagrams;
some examples A_n, B_n, C_n, D_n, SO(n,m), SU(n,m); and elementary lattices | ||
| Lie Groups: | Relationship between algebra and group; topology; decompositions | ||
| Representations: | Weight lattices; highest-weight representations, infinite-dimensional realizations | ||
| Symplectic geometry: | Sergio, Animesh, Matt, or Seth might give lectures. | ||
| Differential Geometry: 6 weeks [or less] | early part by Finley | ||
| Manifolds, tangent bundles, differential forms (as co-vectors), Grassmann products | |||
| Fiber bundles, connections in bundles; jet bundles | |||
| Real and complex projective spaces. | Aaron, Pat, or Collin | ||
| Algebraic Geometry: 1-2 weeks | |||
| functions over algebraic Riemann surfaces | by Finley | ||
| Gröbner bases, polynomial system solving | by Steve | ||
| real and complex projective spaces | perhaps by Pat | ||
| Category Theory: 1-2 weeks | Aaron | ||
A possible following semester, perhaps should include more Lie groups and algebras, and some homology and cohomology.
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