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CATEGORIES:Applied and Computational Analysis Graduate Semina
r
SUMMARY:A topological link between spectral and scattering
theory - Serge Richard (visiting DPMMS from Unive
rsity of Lyon 1)
DTSTART;TZID=Europe/London:20081024T140000
DTEND;TZID=Europe/London:20081024T150000
UID:TALK14656AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/14656
DESCRIPTION:During this seminar\, we shall start by recalling
the definitions of the main objects of spectral an
d scattering theory. We shall then introduce a com
mon\nversion of Levinson's theorem that appears in
the literature and discuss its meaning. This theo
rem establishes a relation between the number of b
ound\nstates of a quantum system and an expression
in terms of the scattering operator. Its precise
form\, however\, depends on various conditions\, s
uch as the\ndimension of space or the existence of
resonances at thresholds\, and also on a regulari
sation procedure. We shall then propose a differen
t approach of\nthis result that takes care of the
corrections and of the regularisation automaticall
y. Our approach means\, above all\, a change of pe
rspective in that we\ninterpret Levinson's theorem
as a relation between a bulk and a boundary topol
ogical invariant. This also makes clear that Levin
son's theorem is in fact\nan index theorem.\n
LOCATION:MR14\, Centre for Mathematical Sciences\, Wilberf
orce Road\, Cambridge
CONTACT:
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