## SPRING SCHOOL in discrete probability, ergodic theory and combinatorics

**April 4 - 15, 2011, Graz**

General program (pdf) of the spring school and Detailed Program (pdf). Participants list: pdf file.

Accomodation in Pension Stadthalle Johannes, Graz and in the Guest house of Graz University of Technology. The list of participants accomodated in Pension Johannes (pdf) and in the Guest house of TU.

You can check in in Pension Johannes until 9:00 pm. If you arrive later, please let us know before. We can maybe pick up the keys for your room, and put them in a safe, near the main entrance door. For the participants accomodated in the guest house: there is no reception there. We will fetch the keys a few days before your arrival, and then meet you on Sunday in the city or at the mathematics institute.

#### Main lectures by:

- Geoffrey Grimmett
(Cambridge)

*Uniform spanning trees and other random animals.***Abstract:**Spanning trees, self-avoiding walks, connected clusters, entanglements: these are classes of graphs which, when chosen randomly, possess especially rich probabilistic structure. Their study impacts on such topics as combinatorics, geometry, and interacting systems in probability and physics. Some of their basic theory will be developed in these lectures. - Jeffrey Steif
(Göteborg)

*Noise sensitivity and percolation. Lecture Notes here***Abstract:**In these lectures, I will introduce the notions of noise sensitivity and noise stability for Boolean functions. Many examples will be given. Discrete Fourier analysis plays a central role in this theory. One of the main examples illustrating noise sensitivity is crossing events in percolation theory which will be described in detail. There are three methods to studying sensitivity of percolation; hypercontractivity, randomized algorithms and the geometric study of the spectrum. - Anders Karlsson
(Geneva)

*Discrete heat kernels and applications.***Abstract:**In my lectures I will define heat kernels on graphs and deduce a general expression for the heat kernel on Cayley graphs in terms of Bessel functions. There is also a spectral expression for the heat kernel. Equating these two expressions gives formulas which via certain transformations eventually lead to several applications. These are relevant for some questions in combinatorics, differential geometry, number theory, and statistical physics. - Michael Björklund
(Zürich)

*Ergodic theory in additive combinatorics.***Abstract:**The aim of the course is to introduce some useful techniques in ergodic theory for studying problems in additive combinatorics. After a crash course in ergodic theory, we will discuss Furstenberg's approach to Szemeredi's theorem, recent advances on this topic, and how some questions about product sets in groups can be understood via stationary processes.

- Ecaterina Sava (TU Graz)
- Wolfgang Woess (TU Graz)

This international spring school is primarily addressed to and open for PhD students. The number of places is limited. According to availability, also young PostDocs may be admitted. Partial support may be available.

*"spring school"*,

specifying:

*name*,

*status*(PhD or PostDoc),

*university*and

*country*of origin, and whether participation is subject to availability of

*funding*.

Planned structure of the program:

Morning - lectures by (some of) the 4 lecturers.

Afternoon - exercise classes; shorter talks by young participants
on their work.

(This is not planned as a conference in disguise,
but should have a true educational character.)

More details will follow.

### Poster

The workshop poster (pdf | 600dpi png).