Pantheon SEMPARIS Le serveur des séminaires parisiens Paris

Status Confirmed
Seminar Series SEM-DARBOUX
Subjects cond-mat,hep-th,math.MP
Date Thursday 4 February 2021
Time 11:00
Institute LPTHE
Seminar Room bibliothèque du LPTHE, tour 13-14, 4eme étage
Speaker's Last Name Kellendonk
Speaker's First Name Johannes
Speaker's Email Address kellendonk [at] math [dot] univ-lyon1 [dot] fr
Speaker's Institution Institut Camille Jordan, Université Claude Bernard Lyon 1
Title The non-commutative topological approach to topological phases with protecting symmetry
Abstract In this talk we review the K-theoretic 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 well-defined, 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 K-theory and its dual (K-homology or cyclic cohomology) to describe the topological phases and their numerical topological invariants.
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