MONDAY 23rd May, 2-3PM, Lecture Theatre 4A, Building 54
THE DIRAC OPERATOR
The Dirac operator of R^n will be defined. This is a first order elliptic differential operator with constant coefficients.
Next, the class of differentiable manifolds which come equipped with an order one differential operator which at the symbol level is locally isomorphic to the Dirac operator of R^n will be considered. These are the Spin-c manifolds.
Spin-c is slightly stronger than oriented, so Spin-c can be viewed as "oriented plus epsilon". Most of the oriented manifolds that occur in practice are Spin-c. The Dirac operator of a closed Spin-c manifold is the basic example for the Hirzebruch-Riemann-Roch theorem and the Atiyah-Singer index theorem.
TUESDAY 24th May, 2-3PM, LECTURE THEATRE 4A, Building 54
This is an expository talk about the Atiyah-Singer index theorem. Some low dimensional examples of the theorem will be considered. The Dirac special case of the theorem will be proved, with the proof based on Bott periodicity. The proof will be outlined that the Dirac special case implies the full theorem.
"A quick reminder about next week’s GGSE in Oxford. First, we’re delighted to announce that Jim Howie will also talk. The programme is as follows.
Location: Lecture Theatre 6, Andrew Wiles Building, Oxford
2pm Jim Howie (Heriot—Watt): 1-relator quotients of free products
3.15pm: Ashot Minasyan (Southampton): Conjugacy separability of non-positively curved groups
4.30pm: Henry Wilton (Cambridge): Essential surfaces in graphs
NOTE the later-than-usual start time.
As usual, further information, including times, locations and abstracts, will be available on the website: http://www.ucl.ac.uk/~ucahllo/ggse/ .
And finally, if you're a parent who may have difficulty attending the meeting, please don't forget about LMS childcare grants: http://lms.ac.uk/grants/childcare-supplementary-grants.
We’re looking forward to seeing you there!
The meeting will include the following mini-courses
Asymptotic dimension of mapping class groups, Mladen Bestvina,
Dimension local and global, Alexander Dranishnikov
Decomposing spaces and actions, Erik Guentner
Limited funding is available for applications before May 15th.
Wednesday 9th-Saturday 12th March I will be attending Indira Chatterji's workshop at the Laboratoire Dieudonné de l'Université de Nice, on Boundaries of CAT(0) Cube Complexes. Mark Hagen and Michah Sageev will be delivering mini-courses on the simplicial, Roller and Poisson boundaries on Thursday and Friday.