Introduction to Gaussian fields and multiplicative chaos, spring 2017

Last modified by saksman@helsinki_fi on 2024/03/27 10:29

Introduction to Gaussian fields and multiplicative chaos, spring 2017

Scope: 10 cr

Type: Advanced studies

Teaching: Lectures (Mo 10-12), Tu 12-14 and We 10-12 C124 at Exactum. First lecture on Tuesday 17.1.17.

Topics: Gaussian fields are fundamental objects that play an important role in many different connections. They are used extensively e.g. inside various branches of mathematics, in stochastic modelling, and many areas of mathematical physics including scaling limits of lattice models like SLE.

The aim of the first part of the course is to provide the basic ingredients of the general theory of Gaussian random fields. The second part aims somewhat deeper and e.g. discusses in more detail basic properties of Gaussian free fields. Finally, the course ends by giving an introduction to multiplicative chaos. These fascinating measures appear in e.g. in connection with scaling limits of statistical physics, mathematical finance, turbulence, and quantum gravity. If time permits, we will describe how they appear also in connection with the Riemann zeta function.

Prerequisites: Probability theory 1 and 2 (not all of the material is needed), or equivalent knowledge.

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News

Course is over, thank's for participation!

Exercises

List of exercises

Teaching schedule

Most of the weeks 3-9 and 11-18, (Mondays 10-12), Tuesdays 12-14 and Wednesdays 10-12 in room C124.

Easter holiday 13.-19.4.

Passing the course

The course can be passed by attending (most of) the lectures and returning in a written form a portion (around 50 %) of the given exercises. Alternatively, the exercises can be replaced by a written essay on a topic agreed on with the lecturer.