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.