
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 
GutkinKottosSmilansky characteristic equation 
PDF 
Video 
6 
BarraGaspard 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 