Tuesdays, Wednesdays and Thursdays, 10:00-12:00, Room 347.

This site will be a simple repository of the materials from the course.
Problem sheets and other documents will be uploaded here.

You can check the syllabus and the bibliography here. You can also see the bibliography below.

Problem sheets

Problem sheet 0: sample problem.

Problem sheet 1: the tensor product of Clifford algebras and irreducible representations of matrix algebras.

Problem sheet 2: the Clifford algebra of a subspace and the case of V+V*.

Problem sheet 3: the definition of the Spin group and some examples.

Presentations

This is the schedule:

• Thursday 16: Spin: the Physics side.
• Tuesday 21 (10-12h): Dirac Operators in Riemannian Geometry. + 1.
• Wednesday 22 (10-12h): On the spinor representation of surfaces in Euclidean space. Spin structure, the Dirac operator and the Atiyah-Singer index theorem on four-manifolds.
• Wednesday 22 (15-17h, ROOM 232!): Spinor construction of vertex operator algebras. Spinor bundles over curves.
• Thursday 23 (9-13h): A universal approach to Clifford algebras. Clifford algebras, Bott periodicity and K-theory. Clifford algebras in characteristic 2.

Bibliography

1. J. Figueroa-O’Farrill. Spin Geometry. Lecture notes, available at http://empg.maths.ed.ac.uk/Activities/Spin or here, 2010.
2. T. Friedrich. Dirac operators in Riemannian geometry, volume 25 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 2000.
3. D. J. H. Garling. Clifford algebras: an introduction, volume 78 of London Mathematical Society Student Texts. Cambridge University Press, Cambridge, 2011.
4. F. R. Harvey. Spinors and calibrations, volume 9 of Perspectives in Mathematics. Academic Press, Inc., Boston, MA, 1990.
5. H. B. Lawson, Jr. and M.-L. Michelsohn. Spin geometry, volume 38 of Princeton Mathematical Series. Princeton University Press, Princeton, NJ, 1989. Available online at www.indiana.edu/∼jfdavis/teaching/m721/resources/spingeometry.pdf.
6. P. Lounesto. Clifford algebras and spinors, volume 286 of London Math- ematical Society Lecture Note Series. Cambridge University Press, Cambridge, second edition, 2001.
7. E. Meinrenken. Clifford algebras and Lie theory, volume 58 of A Series of Modern Surveys in Mathematics. Springer, Heidelberg, 2013. Preliminary online version available at http://isites.harvard.edu/fs/docs/icb.topic1048774.files/clif_mein.pdf .