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SUMMARY:Johannes Kellendonk (Institut Camille Jordan\, Lyon)
DTSTART:20210204T100000Z
DTEND:20210204T113000Z
DTSTAMP:20260423T052621Z
UID:Darboux/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Darboux/2/">
 The non-commutative topological approach to topological phases with protec
 ting symmetry</a>\nby Johannes Kellendonk (Institut Camille Jordan\, Lyon)
  as part of Darboux Seminar\n\nLecture held in Zoom.\n\nAbstract\nIn this 
 talk we review the K-theoretic description of topological phases of insula
 tors and superconductors in the effective one particle approximation. In t
 hat approximation\, an insulator (or superconductor) is described by a Ham
 iltonian whose spectrum has a gap at the Fermi energy. Two Hamiltonians be
 long to the same topological phase if they can be deformed into each other
  without closing the gap. For this to be well-defined\, it is important to
  specify the space of possible Hamiltonians with its topology. When this s
 pace is taken to be a C*-algebra equipped with a real structure and a grad
 ing\, one can use real graded K-theory and its dual (K-homology or cyclic 
 cohomology) to describe the topological phases and their numerical topolog
 ical invariants.\n
LOCATION:https://researchseminars.org/talk/Darboux/2/
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