Student Noncommutative Geometry Seminar

Mondays 4-6pm, 959 Evans

Along with Matt Tucker-Simmons, I helped organize the student NCG seminar at UCB during fall 2007. Many with backgrounds in Banach algebras or C* algebras attended and gave talks. See the math department's archived seminar announcements for more detailed abstracts.

Here are some informal notes that Matt and I compiled.

8/27- Organizational meeting, followed by a survey of key results, and an illustration of the equivariant vector bundle construction, via the Mobius bundle.

8/29- Review of Serre-Swan.

9/3- Labor Day, no meeting

9/10- Theory of equivariant vector bundles, according to Rieffel's recent paper. This approach will provide our first explicit (commutative) examples of spectral triples. Specifically, we will start with the Riemann sphere, via the Hopf fibration.

9/17- Continue with examples, with an eye towards connections, Dirac operators, and spin structures.

9/24- Finish the coset space examples.

10/1- The (reduced) group C* algebras of discrete groups, with Dirac operator given by multiplication by a length function.

10/8- Continue group C* algebras.

10/15- A look at the noncommutative torus.

10/22- An introduction to T-duality.

10/29- Continuing to look at the noncommutative torus.

11/5- Classifying spaces and cohomological classification of locally trivial continuous fields of C* algebras.

11/12- Holiday, no meeting

11/18- Definition and examples of Morita equivalence of C* algebras.

11/25- Continue Morita equivalence. Specifically, we will look at crossed product algebras.