Status  Confirmed 
Seminar Series  SEMDARBOUX 
Subjects  condmat,hepth,math.MP 
Date  Thursday 4 February 2021 
Time  11:00 
Institute  LPTHE 
Seminar Room  bibliothèque du LPTHE, tour 1314, 4eme étage 
Speaker's Last Name  Kellendonk 
Speaker's First Name  Johannes 
Speaker's Email Address  kellendonk [at] math [dot] univlyon1 [dot] fr 
Speaker's Institution  Institut Camille Jordan, Université Claude Bernard Lyon 1 
Title  The noncommutative topological approach to topological phases with protecting symmetry 
Abstract  In this talk we review the Ktheoretic description of topological phases of insulators and superconductors in the effective one particle approximation. In that approximation, an insulator (or superconductor) is described by a Hamiltonian whose spectrum has a gap at the Fermi energy. Two Hamiltonians belong to the same topological phase if they can be deformed into each other without closing the gap. For this to be welldefined, it is important to specify the space of possible Hamiltonians with its topology. When this space is taken to be a C*algebra equipped with a real structure and a grading, one can use real graded Ktheory and its dual (Khomology or cyclic cohomology) to describe the topological phases and their numerical topological invariants. 
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