Probability theory is a branch of mathematics that deals with random phenomena. Such phenomena are studied in a wide variety of different fields, including computer science, physics, chemistry and biology.

The probability seminar aims at exposing students to advanced probability theory and selected applications. One topic will be selected each year. The topic for the academic year 2015-2016 will be Random Matrix Theory. Random Matrix Theory is a flourishing research area aiming to study properties of large matrices with random entries.

A systematic analysis of spectral properties (e.g. distribution of the eigenvalues) of random matrices started within the field of nuclear physics with the seminal work of Eugene Wigner to model the spectra of heavy atoms. More recently Random Matrix theory has became a well established mathematical theory linked with several research areas in theoretical physics as well as in statistics, number theory and combinatorics, and its wide range of applications is still in expansion.

The seminar starts with developing the basic theory from scratch and then moves on to selected applications. The goal of the seminar is that students become familiar with studying and presenting modern probability theory: by listening to lectures, giving presentations themselves, and by writing a small report. The course material is mainly based on key recents monograph and lecture notes (available online). The first few introductory lectures will be given by Avena and Verbitskiy, all other lectures by the participants. Each participant will choose two topics from a list presented at the beginning of the course, and will prepare two lectures on the chosen topics

as well as the handout materials.

**Examination**

The final grade is based on active participation, the two presentations and the hand-out.

**Literature**

1) Manjunath Krishnapur, Lecture Notes on Random Matrix Theory. http://math.iisc.ernet.in/~manju/RMT/RMT.pdf

2) Terence Tao, Topics in Random Matrix Theory https://terrytao.files.wordpress.com/2011/02/matrix-book.pdf

**Preliminary schedule**

DATE SPEAKER

03/09/15 NO LECTURE

10/09/15 AVENA

17/09/15 AVENA

24/09/15 VERBITSKIY

01/10/15 NO LECTURE

08/10/15 VERBITSKIY

15/10/15 Students 1

22/10/15 Students 1

29/10/15 Students 1

05/11/15 NO LECTURE

12/11/15 Students 2

19/11/15 Students 2

26/11/15 Students 2

03/12/15 Students 2

10/12/15 Students 2