# Paul Baum mini course on the Atiyah Singer index theorem

20/05/16 14:15

Prof. Paul Baum, Evan Pugh Professor of Mathematics at Penn State, will be delivering a short course on the Atiyah-Singer index theorem, aimed at a general mathematical audience. If you want to read something about the theorem in advance there is a very short article about it on the Abel Prize website:

Details below:

MONDAY 23rd May, 2-3PM, Lecture Theatre 4A, Building 54

THE DIRAC OPERATOR

TUESDAY 24th May, 2-3PM, LECTURE THEATRE 4A, Building 54

ATIYAH-SINGER REVISITED

__http://www.abelprize.no/c53865/binfil/download.php?tid=53804__Details below:

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

ATIYAH-SINGER REVISITED

*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.*