Your course mark will be based on two items:
- regular attendance
- an essay on some topic related to the theme of this course.
The essay should be around 4 pages, preferably typed. You can pick one
of the topics below, or also suggest a topic yourself. It might be on
some "standard" material that wasn't discussed in class, or also a
summary of some research paper.
The essay is due by December 4, i.e. the last day of classes. (Let me know if you need
extra time.)
Topics:
Classification of the real Clifford algebras Cl(n,m) (see e.g. the
paper by Atiayh-Bott-Shapiro. See also Budinich-Trautman, "The
spinorial chessboard", or Gracia-Bondia et al, "Elements of noncommutative
geometry".)
Weyl algebras and the metaplectic representation (this may be
viewed as the 'symplectic' counterpart to Clifford algebras and the
Spin representation). (E.g.: Books by Lion-Vergne and Crumeyrolle,
paper by Rawnsley-Robinsohn.)
Clifford algebras and K-theory (The paper by Atiyah-Bott-Shapiro)
Clifford algebras and Thom forms (Mathai-Quillen construction)
(The paper by Mathai-Quillen)
The Hopf-Koszul-Samelson theorem (invariants in \wedge\g, for \g
a semisimple Lie algebra) (The book by Greub-Halperin-Vanstone,
volume III)
The Kostant-Hopf-Koszul-Samelson theorem (Invariants in Cl(\g), for
\g a semisimple Lie algebra) (Kostant's paper on "A Clifford algebra
analogue..")
Octonions and G_2. (See e.g. the paper by John C. Baez, "the octonions")
Clifford algebras in inifinite dimensions (E.g. the book by Plymen-Robinson.)
The Kashiwara-Vergne conjecture. (A generalization of the Duflo theorem.)
(The recent papers by Alekseev-Torossian.)