Ergodic Operators and Quantum Graphs: June 6-10, 2022

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Organized by:

David Damanik (Rice University),

Jake Fillman (Texas State University),

Selim Sukhtaiev (Auburn University)

Ergodic Schrödinger operators have been studied heavily since the 1970s, as they include many examples of physical interest, such as disordered media, electrons in an external magnetic field, and quasicrystals. These operators enjoy many subtle connections to other areas of mathematics, such as dynamical systems, topology, and group theory.

The study of quantum graphs stems from the modeling of thin waveguides arranged into a topological network. Such models appeared already in the 1930s but have experienced a surge in popularity in recent years.

Recent works have exploited connections between these two fields; these developments have scratched the surface of a much larger opportunity for collaboration. Thus, the aim of this workshop is to bring these two communities together for two purposes: to disseminate recent results, and to foster collaboration and communication between these communities.

Talk Schedule


Time Title Speaker Location
8:30am Breakfast SCGP Cafe
9:00am Vertex coupling effects in quantum graph spectra Pavel Exner SCGP 102
10:00am Coffee Break N/A SCGP Cafe
10:30am Fermi isospectrality for discrete periodic Schrödinger operators Wencai Liu SCGP 102
11:30am Small Break N/A SCGP Cafe
11:45am Localization for anisotropic XY spin chain in quasi-periodic magnetic field Rui Han Zoom
12:45pm Lunch N/A SCGP Cafe
2:15pm On the hot spots of quantum graphs Jonathan Rohleder Zoom
3:15pm Tea Time N/A SCGP Cafe
4:00pm Time dependent quantum graphs and the geometric phase Gilad Sofer SCGP 102
4:30pm 1-Dim Half-line Schrödinger Operators with H^{-1} Potentials Xingya Wang SCGP 102

Time Title Speaker Location
8:30am Breakfast SCGP Cafe
9:00am M-functions and metric graphs:hierarchy, inverse problems and magnetic fluxes Pavel Kurasov Zoom
10:00am Coffee Break N/A SCGP Cafe
10:30am The Kronig-Pennet model in a quadratic channel with δ interactions Uzy Smilansky SCGP 102
11:30am Lunch N/A SCGP Cafe
1:00pm Quantum mechanics on graphs:why is it interesting? Pavel Exner N/A
2:15pm Generic Laplace eigenfunctions of finite metric graphs Lior Alon SCGP 102
3:15pm Small Break N/A SCGP Cafe
3:30pm Universality of nodal count statistics in large graphs Gregory Berkolaiko SCGP 102

Time Title Speaker Location
8:30am Breakfast SCGP Cafe
9:00am Magnetic oscillations in a model of (twisted bilayer) graphene Simon Becker Zoom
10:00am Coffee Break N/A SCGP Cafe
10:30am The Maslov index and the spectrum of differential operators Yuri Latushkin SCGP 102
11:30am Small Break N/A SCGP Cafe
11:45am Spectral flows and the Robin count deficiency for metric graphs Ram Band SCGP 102
12:45pm Lunch N/A SCGP Cafe
2:15pm Localization and eigenvalue statistics within Hartree-Fock theory Rodrigo Matos SCGP 102
3:15pm Tea Time N/A SCGP Cafe
4:00pm Laplacians on Infinite Graphs Noema Nicolussi SCGP 102
6:00pm Banquet N/A SCGP Cafe

Time Title Speaker Location
8:30am Breakfast SCGP Cafe
9:00am Two classes of ergodic operators on quantum graphs Selim Sukhtaiev Zoom
10:00am Coffee Break N/A SCGP Cafe
10:30am Spectral Properties of Periodic Elastic Beam Hamiltonians on Hexagonal Lattices Burak Hatinoglu SCGP 103
11:45am Problem Session N/A SCGP 102
12:45pm Lunch N/A SCGP Cafe
2:15pm Spectral approximations beyond dimension one Siegfried Beckus SCGP 102
3:15pm Tea Time N/A SCGP Cafe
4:00pm Eigenvector behavior for graphs from quantized interval maps Laura Shou SCGP 102

Time Title Speaker Location
8:30am Breakfast SCGP Cafe
9:00am Reducibility of the Bloch and Fermi Varieties Stephen Shipman SCGP 102
10:00am Coffee Break N/A SCGP Cafe
10:30am Multiscale Analysis in Momentum Space for Multi-Dimensional Quasi-Periodic Schrodinger Operators Yulia Karpeshina SCGP 102
11:30am Lunch N/A SCGP Cafe