COST Action MAT-DYN-NET

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: https://stockholmuniversity.zoom.us/j/68537577130

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:

• Metric graph as a singular manifold
• Differential operators on graphs
• Characteristic equation and spectrum
• Surgery of graphs
• Standard Laplacians on metric graphs
• Trace formula
• Topology and spectrum
• Reducibility of secular polynomials
• Diophantine analysis and arithmetic structure of the spectrum
• Almost periodic functions and Ambarstumian theorems for graphs
• Introduction to inverse problems
• Stable polynomials and crystalline measures

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	QGraph meeting	PDF	Program
14	Ambartsumian type theorems	PDF	Video

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