Vorträge in der Woche 24.04.2017 bis 30.04.2017
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Dienstag, 25.04.2017: Collapse under bounded curvature
Saskia Roos (MPI Bonn)
Any sequence of closed n-dimensional Riemannian manifolds with bounded sectional curvature and diameter admits a subsequence converging to a compact metric space in the Gromov-Hausdorff topology. If the dimension of the limit is strictly less than n one says that the sequence collapses in the limit. We will discuss the structure of collapsing sequence and give a characterization for collapsing sequences whose limit space has codimension one.
| Uhrzeit: | 14:15 |
| Ort: | C9A03 |
| Gruppe: | OSAZ |
| Einladender: | Deitmar |
Donnerstag, 27.04.2017: (De)localization in topological insulators: A Wannier function approach
Dr. Domenico Monaco
In this talk I will describe how Wannier functions (WFs) provide a powerful tool to investigate localization and transport properties of 2D and 3D gapped periodic quantum systems, including Chern insulators, quantum Hall systems, and time-reversal symmetric (TRS) topological insulators. In the first part of the talk, I will present a "localization dichotomy" for Chern and quantum Hall insulators, stating that either there exist exponentially localized WFs (in which case the Hall conductivity vanishes), or any system of WFs yields a divergent second moment of the position operator; no intermediate regimes are allowed. The second part of the talk will instead be devoted to TRS topological insulators: I will discuss how their Z_2 invariants arise as topological obstructions to the existence of localized and time-reversal symmetric WFs, and how to construct the latter in the unobstructed case.
| Uhrzeit: | 16:15 |
| Ort: | N 14 |
| Gruppe: | Oberseminar Mathematische Physik |
| Einladender: | Hainzl, Keppeler, Teufel, Tumulka |