Abstracts are available here.

We will have the following three lecture courses:

- Will Perkins (University of Birmingham): Gibbs measures, sparse graphs, and optimization

Syllabus. Slides. Lecture notes.

The hard-core model is a basic model from statistical physics in which a gas is represented by a random independent set from a graph. As the typical density of this independent set increases on a lattice like Z^d, the model undergoes a crystallization phase transition from a disordered to an ordered state, representing a freezing phenomenon. While Gibbs measures like the hard-core model were developed in statistical physics, they have proved invaluable in a wide array of scientific disciplines including statistics, machine learning, and combinatorics. In this mini-course, we will focus on the use of Gibbs measures in graph theory and geometry. We will introduce methods that combine ideas from optimization and the theory of local weak convergence to prove results about independent sets and matchings in bounded-degree graphs, as well as sphere packings in Euclidean space. - Oleg Pikhurko (University of Warwick): Descriptive graph combinatorics

We will discuss measurable versions of some classical combinatorial problems (vertex/edge colourings, matchings, etc). Our main objects of study will be so-called graphings, that appear as limit objects for bounded degree graphs. We will mostly concentrate on positive results, where a powerful tool for constructing a measurable satisfying assignment is to design a parallel decentralised algorithm that converges to it almost everywhere. - Guus Regts (University of Amsterdam): Deterministic approximation algorithms for partition functions and zeros of graph polynomials with connections to sparse graph limits

Slides from Guus's lectures are available here

Recently Alexander Barvinok came up with a new approach for approximate counting besides the existing Monte Carlo Markov chain and correlation decay approach. The approach is based on writing the counting problem, e.g. the number of matchings in a graph, as the evaluation of a polynomial $p$ and truncating the Taylor series of $\log(p)$. This approach works well if $p$ has no complex zeros in the domain of interest. Together with Viresh Patel the speaker has shown that this approach leads to polynomial time algorithms essentially when the graphs have bounded degree. In this mini course I will explain Barvinok's approach and the polynomial time speed up for bounded degree graphs. I will show some results concerning zeros of certain graph polynomials. I will focus on concrete examples, most notably the independence polynomial and the permanent. If time permits I will also say something about connections with sparse graph limits.

**Participants:** (as of Feb 23, 2018):
Timothy Chan,
Peter Csikvari,
Endre Csoka,
Ewan Davies,
Martin Dolezal,
Robert Hancock,
Frederik Garbe,
Jan Grebik,
Jan Hladky,
Matthew Jenssen,
Tereza Klimosova,
Daniel Kral,
Jon Noel,
Viresh Patel,
Christos Pelekis,
Will Perkins,
Diana Piguet,
Oleg Pikhurko,
Guus Regts,
Israel Rocha,
Vaclav Rozhon,
Maria Saumell,
Bart Sevenster,
Matas Sileikis,
Jakub Sosnovec,
Fan Wei

Indicate your arrival/departure time and select your meals in a form. I sent a link to the form to all participants on March 22, the title of the email was "Workshop Graph Limits in Bohemian Switzerland: Last minute information".