International Summer School on "Graphs and Spectra"
at the TU Chemnitz, 18--23 July 2011
The schedule of the summer school is as follows:
| 18. July 2011 |
19. July 2011 |
20. July 2011 |
21. July 2011 |
22. July 2011 |
23. July 2011 |
| Monday |
Tuesday |
Wednesday |
Thursday |
Friday |
Saturday |
| 09.30-10.00 registration |
09.30-10.15 Voigt |
09.30-12.30 PhD-Symposium |
09.30-10.15 Voigt |
09.30-10.15 Smilansky |
09.30-12.30 PhD-Symposium |
| 10.00-10.15 opening |
10.30-11.15 Berkolaiko |
|
10.30-11.15 Berkolaiko |
10.30-11.15 Smilansky |
|
| 10.15-11.00 Voigt |
11.30-12.15 Kurasov |
|
11.30-12.15 Kurasov |
11.30-12.15 Luger |
|
| 11.15-12.00 Berkolaiko |
12.15-13.15 break |
|
12.15-13.15 break |
12.15-13.15 break |
|
| 12.00-13.00 break |
|
|
|
|
|
| 13.15-14.00 Voigt |
13.30-14.15 Luger |
14.00-18.00 excursion |
13.30-14.15 Kurasov |
13.30-14.15 Luger |
14.00-18.00 discussion |
| 14.15-15.00 Berkolaiko |
14.30-15.15 Berkolaiko |
|
14.30-15.15 Smilansky |
14.30-15.15 Kurasov |
|
| 15.15-16.00 Kurasov |
15.30-16.15 Schanz |
|
15.30-16.15 Streda |
|
|
| 16.00-18.00 PhD-Symposium |
16.15-18.00 PhD-Symposium |
|
16.15-18.00 PhD-Symposium |
15.15-18.00 PhD-Symposium |
|
The tentative plan for the lectures of the mini-courses is as follows:
| Gregory Berkolaiko: Nodal domains and critical nodal partitions |
| Intoduction to quantum graphs, hearing the shape of the graph, isospectral graphs and nodal domains |
| Rank-one perturbations and interlacing inequalities, variation of graph parameters |
| Bounds and exact formulas for nodal count |
| Critical partitions on graphs |
Scanned notes of mini-course of Gregory Berkolaiko
| Pavel Kurasov:
Inverse problems for quantum graphs |
| Quantum graphs: definition and elementary spectral properties |
| Titchmarsh-Weyl M-function for quantum graphs and spectra
of compact graphs |
| Boundary control and inverse problems for standard
operators on trees |
| Inverse problems for graphs with cycles |
| Isoscattering and matching conditions |
| Annemarie Luger:
Analytic matrix functions as a tool for quantum graphs |
| On the different (but equivalent) ways how to write s.a.
boundary/matching conditions: a comparison and overview |
| Kreins formula and its application to quantum graphs |
| On the number of negative eigenvalues of Laplacians on graphs |
| Uzy Smilansky: Topics from the spectral theory
of the discrete Laplacian on d-regular graphs |
| Introduction to d-regular graphs |
| The Bartholdi identity and spectral trace formulae. Applications for metric (quantum) graphs |
| Spectral statistics |
| Eigenvectors, nodal domains and percolation |
| Scattering on discrete graphs |
Slides of extended version of mini-course of Uzy Smilansky
- lecture
- lecture
- lecture
- lecture
- lecture
| Jügen Voigt: Differential operators on metric graphs and selfadjointness |
| Forms and self-adjoint operators on Hilbert space |
| Dirichlet forms and Beurling-Deny criteria |
| Boundary (or glueing) conditions for second order
differential operators on metric graphs (quantum graphs) |
| On positivity of the associated `Schrödinger semigroup' |
Scanned notes of mini-course of Jürgen Voigt
pdf-file
Physics lectures
| Pavel Streda: Anomalous Hall conductivity: local orbitals approach |
| A review of general features of the anomalous Hall conductivity
observed on ferromagnetic systems followed by a theory
based on the space distribution of the current densities
will be presented. It is argued that intrinsic anomalous
conductivity is determined by the Berry phase correction
to the magnetic moment which is closely related to the charge
polarizability. Effect of the finite electron life time is
modeled by energy fluctuations of atomic-like orbitals.
Presented tight-binding model gives by the unified way
experimentally observed qualitative features of the anomalous
Hall conductivity in the so called good metal regime and that
called as bad metal or hopping regime. Posibility to describe
this effect in the high conductivity regime by using Landauer-
Buttiker type transport theory will be discussed. |
| Holger Schanz:
Semiclassical expansion of correlation functions on quantum graphs:
Applications to mesoscopic electron transport
|
| The physical mechanism of electronic transport changes qualitatively
when a device such as a transistor is downsized to the nanometer
scale. Then the transport is mesoscopic and both, classical and
quantum aspects are relevant simultaneously. In this regime, one
approach to a quantitative theory is based one a semiclassical
summation over classical trajectories. Quantum graphs are useful
models in this context because they allow to test the summation
techniques in a simplified situation, where the enumeration of
trajectories and the calculation of their phases is exact. In the talk
I will demonstrate this point with two examples of physical interest,
Anderson localization in 1D disordered systems and electronic shot noise
for a chaotic quantum dot.
|
Kontakt
Adresse
TU Dortmund
Fakultät für Mathematik
Lehrstuhl IX
Vogelpothsweg 87
44227 Dortmund
Sie finden uns auf dem sechsten Stock des Mathetowers.
Sekretariat
Janine Textor (Raum M 620)
Tel.: (0231) 755-3063
Fax: (0231) 755-5219
Mail: janine.textor@tu-dortmund.de
Bürozeiten:
Di. und Do. von 8 bis 12 Uhr
Home Office:
Mo. und Fr. von 8 bis 12 Uhr
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