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Status |
Confirmed |
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Seminar Series |
SEM-DARBOUX |
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Subjects |
cond-mat,hep-th,math.MP |
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Date |
Thursday 4 February 2021 |
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Time |
11:00 |
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Institute |
LPTHE |
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Seminar Room |
bibliothèque du LPTHE, tour 13-14, 4eme étage |
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Speaker's Last Name |
Kellendonk |
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Speaker's First Name |
Johannes |
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Speaker's Email Address |
kellendonk [at] math [dot] univ-lyon1 [dot] fr |
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Speaker's Institution |
Institut Camille Jordan, Université Claude Bernard Lyon 1 |
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Title |
The non-commutative topological approach to topological phases with protecting symmetry |
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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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