Lecturer: Pavel Kurasov October 5 - 13, 2010
First meeting: October 5, 13.15 in MH:309A
Quantum graphs denote a wide class of models used to describe systems
where the dynamics is confined to a neighborhood of graph-like structures.
Such models have natural applications in nanosystems, but related methods are
useful in other fields such as microwave networks, chemistry,
and even medicine.
This course will give an introduction into the theory of quantum graphs
considered as ordinary differential equations on metric graphs. Their
spectral and scattering properties will be investigated. In particular we
are going to discuss how geometric properties of graphs are reflected by
the spectrum of the corresponding differential operators. The corresponding
inverse problems will be discussed in details.
Introduction to quantum graphs: definitions and elementary properties
(Tuesday, 5/10, 13:15, MH:309A)
Spectral properties of quantum graphs
(Wednesday, 6/10, 13:15, MH:309A)
Inverse spectral and scattering problems for quantum trees
(Thursday, 7/10, 15:15, MH:309A)
Inverse problems for graphs with cycles
(Monday, 11/10, 15:15, MH:309A)