KO-4   Tuesday July 9 - 15:30

MS6 Part 2 of 2 - Spectral theory and PDEs for metric graphs

MS6 Part 1 of 2

The minisymposium focuses on recent progress in a new area of mathematical physics and applied analysis, namely, on spectral theory and differential equations defined of metric graphs. Studies of physical systems which are either made low-dimensional or discrete for the purposes of computations or inherently built on networks are rapidly growing. The subject of differential equations on metric graphs (or "quantum graphs") which model waveguides, nanotubes, and many other devices is the area where the tools of spectral theory, dynamical systems, and analysis of PDEs have to be adapted to the new setting of increased geometric complexity. Some recent progress in this area will be presented by mostly junior mathematicians specializing on linear and nonlinear theory of quantum graphs. Speakers of the minisymposium will cover various aspects of eigenvalue estimates for the Laplace operator on graphs, localization of eigenfunctions of the Schrodinger equation (both linear and nonlinear), nodal domains, quantum resonances, and existence and stability of nonlinear waves on graphs.

Dmitry Pelinovsky
Gregory Berkolaiko

15:30 - 16:00 - Dmitry Pelinovsky - Unstable drift of spectrally stable shifted states on star graphs [Abstract]

16:00 - 16:30 - Matthias Hofmann - On the existence of solutions to nonlinear equations on metric graphs via energy methods [Abstract]

16:30 - 17:00 - Junping Shi - Existence of solutions for the nonlinear Schr\"odinger equation on metric graphs in supercritical case [Abstract]

17:00 - 17:30 - Anna Maltsev - Localization and landscape functions on quantum graphs [Abstract]

17:30 - 18:00 - Francesca Cottini - Random evolution on combinatorial and metric graphs [Abstract]