Fiches de cours

Summer School on Generalized Curvature (2018)


Lecturer(s) :

Troyanov Marc




Only this year


Next time: From Sept. 2 to Sept. 7, 2018


The goal of this school is to give an introduction for non experts to several contemporary notions of curvatures for metric spaces.


Over the last few decades, there has been intense research on various notions of curvature for non-smooth spaces. The aim of this school is to introduce some aspects of generalized curvatures on metric spaces, graphs, and polyhedra.

The following subjects will be covered: Lipschitz-Killing curvatures, discrete conformal maps, spectral theory of graphs, metric spaces with bounded curvature and surfaces with bounded integral curvature in the sense of Alexandrov.

Besides the main courses,  several talks by researchers active in the domain of the school will be given.

The target audience for this school are PhD students and postdocs interested in geometry and related subjects.


There will be 5 minicourses :

Andreas Bernig (Francfort)      Lipschitz-Killing curvatures.

Matthias Keller (Postdam)       Upper curvature bounds and spectral theory.

Marc Troyanov (EPFL)            Alexandrov surfaces with bounded integral curvature.

Thomas Richard (Paris-Est)    Intrinsic geometry of metric spaces with curvature bounded from below.

Boris Springborn (Berlin)         Discrete conformal maps.


8 additional lectures will be given by expert working in the field of singular or discrete geometry and some interactive workshops will be organized.



Géométrie Métrique, Espaces Singuliers, Courbures de Lipschitz-Klling, Courbure Discrete.

Learning Prerequisites

Recommended courses

Some familiarity with basic differential geometry and metric space geometry.

Learning Outcomes

By the end of the course, the student must be able to:



The book by L. Najman and P. Romon "Modern Approaches to Discrete Curvature" Springer 2017. More references will be given.

Ressources en bibliothèque

In the programs

    • Semester
    • Exam form
       Oral presentation
    • Credits
    • Subject examined
      Summer School on Generalized Curvature (2018)
    • Number of places
    • Lecture
      23 Hour(s)
    • Practical work
      6 Hour(s)

Reference week

      Exercise, TP
      Project, other


  • Autumn semester
  • Winter sessions
  • Spring semester
  • Summer sessions
  • Lecture in French
  • Lecture in English
  • Lecture in German