## Adam Timar, University of Iceland

Math colloquium

**Fyrirlesari: **Adam Timar, Háskóli Íslands

**Titill: **Uniform Spanning Forests of infinite graphs**.**

Staðsetning: Via Zoom. Link to be sent.

Tími: Föstudag 30.október kl.10:00

#### Ágrip:

Consider a spanning tree of a given finite graph, chosen uniformly at random. The so-defined Uniform Spanning Tree (UST) has long been an object of interest, since it is intimately connected to harmonic functions on the graph and random walks.

Given an infinite graph G, such as a cubic lattice, one can take its exhaustion by finite graphs G_n and consider a suitably defined limit of the UST of G_n. The limiting measure is called the Uniform Spanning Forest of G. The resulting random object has had crucial importance in statistical physics on 2 dimensional lattices, but also turned out to be interesting when G is a Cayley graphs of a group. Among other uses, it allows for a simple probabilistic interpretation of an intricate geometric parameter.

The talk will be addressed to a general math audience. We will give a brief overview of the above topics, and present some recent results that are joint work with Gábor Pete.