BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:A topological link between spectral and scattering theory - Serge 
 Richard (visiting DPMMS from University of Lyon 1)
DTSTART:20081024T130000Z
DTEND:20081024T140000Z
UID:TALK14656@talks.cam.ac.uk
CONTACT:4520
DESCRIPTION:During this seminar\, we shall start by recalling the definiti
 ons of the main objects of spectral and scattering theory. We shall then i
 ntroduce a common\nversion of Levinson's theorem that appears in the liter
 ature and discuss its meaning. This theorem establishes a relation between
  the number of bound\nstates of a quantum system and an expression in term
 s of the scattering operator. Its precise form\, however\, depends on vari
 ous conditions\, such as the\ndimension of space or the existence of reson
 ances at thresholds\, and also on a regularisation procedure. We shall the
 n propose a different approach of\nthis result that takes care of the corr
 ections and of the regularisation automatically. Our approach means\, abov
 e all\, a change of perspective in that we\ninterpret Levinson's theorem a
 s a relation between a bulk and a boundary topological invariant. This als
 o makes clear that Levinson's theorem is in fact\nan index theorem.\n
LOCATION:MR14\,  Centre for Mathematical Sciences\, Wilberforce Road\, Cam
 bridge
END:VEVENT
END:VCALENDAR