Bram Petri

Random Methods in Geometry

Practical information


Random methods provide a way to answer questions of the form: "what does a typical [insert your favorite object here] look like?" A classical example is the theory of random graphs. Random graphs have not only been used to study the typical behavior of large graphs but also to provide existence proofs. The latter application is often called "the probabilistic method". The idea of this method is that it is sometimes easier to show that certain behavior appears with a non-zero probability (in a suitable model) than to explicitly construct objects that exhibit this behavior.

The goal of this course will be to discuss applications of these methods in geometry. Subjects will include: The list above is however subject to change depending on the audience.


Lecture notes

I will post my notes here after each lecture. The exercises for every week can be found on the last pages of these notes.
DISCLAIMER: I do not guarantee in any way that these notes are correct. I will be happy to hear of any mistakes that are found.

The complete set of notes can be found here.

The (less up to date) versions that were posted weekly are here:

Exam material

Here is a note that gives an overview of what you are expected to know for the exam. As a general rule, you should not worry if you have understood the material and are able to do the exercises.


Probability theory: Graph Theory: Hyperbolic geometry: Random surfaces: