The Laplacian on metrized graphs
The aim of this course is to study the Laplacian operator, which is a fundamental tool in potential theory, on metrized graphs. After constructing it, we will see some of its basic properties. Next, we will explain how acts the Laplacian on some spaces (like the space of continuous, piecewise affine real-valued functions on a metrized graph, the Zhang space etc) and we will also prove some strong statements, like the Mass formula.
Lecturer
Date
24th March ~ 16th June, 2026
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Tuesday | 13:30 - 16:55 | A3-2-301 | ZOOM 2 | 638 227 8222 | BIMSA |
Prerequisite
None
Syllabus
Class 1 - Class 2: We will introduce some general definitions (and examples) coming from graph theory.
Class 3: Construction of the Laplacian operator on metrized graphs.
Class 4 - Class 12: Study of the Laplacian and introduction to the potential theory (potential kernel, Zhang space, mass formula etc).
Class 3: Construction of the Laplacian operator on metrized graphs.
Class 4 - Class 12: Study of the Laplacian and introduction to the potential theory (potential kernel, Zhang space, mass formula etc).
Reference
The main reference for this course will be the third chapter of Baker and Rumely's book "Potential theory and Dynamics on the Berkovich Projective Line" .
Audience
Advanced Undergraduate
, Graduate
, Postdoc
, Researcher
Video Public
Yes
Notes Public
Yes
Language
English
Lecturer Intro
Arnaud Plessis is an assistant professor at BIMSA from September 2023. His research is mainly focused on diophantine geometry. He obtained his Phd. thesis in 2019 at Université de Caen Normandie. Before joining BIMSA, he has been Attaché Temporaire d'Enseignement et de Recherche (a kind of postdoctoral with course duties) at Université Grenoble Alpes from September 2019 to August 2020. Then, he has been postdoctor at Morningside Center of Mathematics, Chinese Academy of Sciences, from September 2020 to August 2023.