[geometry-ml:01181] Seminar at IPMU on 12/14 Richard

[Satoshi Kondo]

Dear colleagues:

We announce the following seminar at IPMU
(the Institute for the Physics and Mathematics of the Universe).

Regards,

Satoshi Kondo (IPMU)
http://ipmu.jp/
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Speaker: Serge Richard (U.Lyon, Tsukuba U)
Time: Dec 14 (Tue), 13:15-14:45
Place: Seminar room A
Title: Wave operators and a topological version of Levinson's theorem
Abstract:
During this seminar, we shall first recall the definitions of the main
objects of scattering theory. We shall then introduce a common version of
Levinson’s theorem that appears in the literature and discuss its meaning.
This theorem establishes a relation between the number of bound states of
a quantum system and an expression in terms of the scattering operator.
Its precise form, however, depends on various conditions, such as the
dimension of space or the existence of resonances at thresholds, and also
on a regularisation procedure.

We shall then propose a different approach of this result that takes care
of the corrections and of the regularisation automatically. In particular,
we shall show how K-theory for C*-algebras leads to a topological version
of Levinson’s theorem. Our approach means, above all, a change of
perspective which makes clear that Levinson's theorem is in fact an index
theorem. Various examples will be presented and the role of the wave
operators will be emphasized.
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You can check the location from
http://www.ipmu.jp/access/img/KashiwaCampusMap.png
The schedule of the seminar can be checked from
http://db.ipmu.jp/seminar/