Spectral Geometry of Graphs
This course gives an introduction to the geometry of metric graphs and their spectral properties.
Specific contents: Metric graph as a singular manifold, differential operators on graphs, characteristic equation and spectrum, surgery of graphs, Laplace operator on metric graphs, trace formula, topology and spectrum, reducibility of secular polynomials, Diophantine analysis and the arithmetic structure of the spectrum, almost periodic functions and Ambarstumian's theorems, introduction to inverse problems, stable polynomials and crystalline measures.
The course consists of one module.
Teaching Format
Teaching consists of lectures.
Assessment
Assessment takes place through written reports and oral exam.
Examiner
The schedule will be available no later than one month before the start of the course.
We do not recommend print-outs as changes can occur. At the start of the course,
your department will advise where you can find your schedule during the course.
Note that the course literature can be changed up to two months before the start of the course.
Pavel Kurasov, Spectral geometry of graphs, Birkhäuser, 2022.
Course reports are displayed for the three most recent course instances.
