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In the concentration period "CFT: Relations to Subfactors and
Noncommuative Geometry" from November 1 to December 15,
we have lectures of Nigel Higson as follows.

Lecturer: Nigel Higson (Pennsylvania State University)

Title: Index theory, groupoids and noncommutative geometry

Time: Monday, Wednesday 14:00-16:00
and Friday 10:30 - 12:30, two weeks starting from November 24

Abstract:
This course will be about the Atiyah-Singer index theorem, its
treatment from the perspective of noncommutative geometry, and various
extensions of the index theorem that are made possible by
noncommutative geometry. Most of the course will be organized around
the concept of smooth groupoid, which will be a bridge between
standard and noncommutative geometry. We shall present Connes' proof
of the index theorem using the tangent groupoid, and then discuss
equivariant index theory and the Baum-Connes conjecture. At the end
we shall take a look at "local" approaches to index theory using
cyclic cocycles.

Prerequisites include an acquaintance with Hilbert space theory, basic
spectral theory, smooth manifolds, vector bundles and differential
forms. Some prior contact with K-theory in one form or another will
be very helpful, but not essential.

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