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SUMMARY:Bram Mesland (Leiden University)
DTSTART:20201125T200000Z
DTEND:20201125T210000Z
DTSTAMP:20260420T052656Z
UID:NYC-NCG/32
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NYC-NCG/32/"
 >Gabor frames and Wannier bases from groupoid Morita equivalences</a>\nby 
 Bram Mesland (Leiden University) as part of Noncommutative geometry in NYC
 \n\n\nAbstract\nA key question in Gabor analysis is the reconstruction of 
 elements in a Hilbert space \nvia a Gabor frame. Gabor frames arise from a
  finite set of vectors acted upon by a canonically defined \nset of operat
 ors (typically translation and modulation). \nThis data is often convenien
 tly encoded in the algebraic structure of a groupoid. In this talk we will
  discuss how the natural notion of Morita equivalence of groupoids gives r
 ise to Gabor frames for the Hilbert space localisation of \nthe Morita equ
 ivalence bimodule of the reduced groupoid $C^*$-algebras. For finitely gen
 erated and projective submodules\, we show these Gabor frames are orthonor
 mal \nbases if and only if the module is free. \nIf time allows\, we will 
 discuss an application of this result to spectral subspaces of Schroedinge
 r operators with atomic potentials supported on (aperiodic)  Delone sets.\
 n\nThis is joint work with Chris Bourne (Tohoku University)\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/32/
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