Index Theory Seminar

Speaker: Masoud Khalkhali (Western)

"The heat equation proof of the Atiyah-Singer index theorem II"

Time: 11:00

Room: MC 108

The starting point for the heat equation proof of the Atiyah-Singer index theorem is the celebrated McKean-Singer formula and the asymptotic expansion of the heat kernel. In this first lecture the following topics will be covered: basic Sobolev space theory, including Garding's inequality; finiteness and regularity results for elliptic PDE's on compact manifolds, Hodge decomposition theorem for elliptic complexes, existence of the heat kernel and its asymptotic expansion. (Talk 2 of 3)

Comprehensive Exam Presentation

Speaker: Ivan Kobyzev (Western)

"Some calculations of Orlov Spectra"

Time: 13:00

Room: MC 108

Noncommutative Geometry

Speaker: Mitsuru Wilson (Western)

"Toric deformation of a compact Riemannian manifold "

Time: 14:30

Room: MC 108

In 2001, Connes and Landi proved that certain classes of Riemannian manifolds admits an isospetral deformation defined by the isometric toric action. This construction is a vast generalization of NC tori and does include the NC tori. In my talk I will outline the idea and discuss possible consequences.

Index Theory Seminar

Speaker: Masoud Khalkhali (Western)

"The heat equation proof of the Atiyah-Singer index theorem III"

Time: 14:00

Room: MC 107

The starting point for the heat equation proof of the Atiyah-Singer index theorem is the celebrated McKean-Singer formula and the asymptotic expansion of the heat kernel. In this first lecture the following topics will be covered: basic Sobolev space theory, including Garding's inequality; finiteness and regularity results for elliptic PDE's on compact manifolds, Hodge decomposition theorem for elliptic complexes, existence of the heat kernel and its asymptotic expansion. (Talk 3 of 3)