Master course
Spectral Geometry of Graphs   MM7032

Dept. of Mathematics, Stockholm University

Lectures:   Thursdays 16:15-18:00     Cramer room, building 1, Albano
Exercise class: Thursdays 15:15-16:00     Cramer room, building 1, Albano
Permanent ZOOM link:

The lectures are given live in Stockholm with possibility to follow via ZOOM.
Lecture notes for all lectures are distributed directly to all registered students.

Preliminary contents of the course: The lectures will follow the book P. Kurasov "Spectral Geometry of Graphs " under publication by Birkhäuser/Springer.

Interested students will have a possibility to attend
QGraph meeting
on December 8-9, 2022 (13:00-18:00).

Recordings of the lectures and selected lecture notes:
Title of the lecture Lecture notes Video recording
1 How to define differential operators on metric graphs PDF Video
2 Vertex conditions I PDF Video
3 Vertex conditions II PDF Video
4 Elementary spectral properties of quantum graphs PDF Video
5 Gutkin-Kottos-Smilansky characteristic equation PDF Video
6 Barra-Gaspard secular polynomials PDF Video
7 Distribution theory and Poisson's summation formula PDF Video
8 Trace formula I: a proof PDF Video
9 Trace formula II: examples and generalisations PDF Video
10 Trace formula and inverse problems PDF Video
11 Arithmetic structure of the spectrum and crystalline measures PDF Video
12 Spectral gap PDF Video (1st hour)
13 PDF Video
14 PDF Video

Please inform Pavel Kurasov in case you watch videos from this lecture course.