After successful completion of the course, students are able to...

give a presentation on an advanced topic in probability theory, to put the topic into a wider context of modern resarch, and to discuss with the audience.

This year, the topic of the reading seminar will be "Polymers in random environment" and it will be based on the book "Directed polymers in random environments" by Francis Comets. Polymers in random environment are a very active topic of research in mathematical statistical physics and they are related to other areas of mathematics and mathematical physics: stochastic interface growth, disordered systems, random walks... They are also a very rich mathematical object, showing a variety of different large-scale phenomena: scaling limits, phase transitions, invariance principles, localization by disorder, etc. Altogether, this topic will be a very good introduction to the wider topic of mathematical statistical physics and in particular to models with quenched disorder

There will be first a couple of lectures by F. Toninelli to introduce the topic of directed polymers in random environment, and the wider mathematical context. After that, the students will  give presentations (based on Comets' monograph) followed by discussion.

Lectures will take place in English. They will take place in person (with no streaming or recording); only in case of new lockdown they will be online

The proposed schedule of the course could be changed if several students have constraints at the proposed day/time. This will be discussed during the first lecture.

 Most likely, the presentations will take place every two weeks (90 minutes each time). That will depend on the number of participants.

 Office hours for students: Tuesdays 2 p.m. - 3 p.m. 

Presentation by students

Measure and probability theory. Preferably some knowledge of stochastic processes (random walks)