Meistaraprófsfyrirlestur

### Arnbjörg Soffía Árnadóttir

Title: Group actions on infinite digraphs and the suborbit function

Location: Naustið, Endurmenntun.

Time: Thursday October 6. 2016 at 16:00.

### Abstract:

We study infinite directed graphs, using group actions. We start by defining a group homomorphism called the suborbit function. Then we use this homomorphism to investigate various properties of infinite digraphs, including homomorphic images, highly arc transitive digraphs, Cayley-Abels digraphs and the growth of digraphs.

Advisors: Professor Rögnvaldur G. Möller and professor Jón Ingólfur Magnússon at Science Institute, University of Iceland.

Examiner: Professor emeritus Peter M. Neumann The Queen’s College, Oxford University.

Math Colloquium

### Speaker: Matthias Hamann

Title: Accessible groups and graphs

Location: V-157, VRII.

Time: Friday, October 2, at 15:00-16:00.

### Abstract:

The talk falls into two parts. First, we give an overview of the group theoretical concept of accessibility and the main results in this area.

In the second part, we define the graph theoretical notion of accessibility. After a brief discussion of the connection of these two kinds of accessibility, we reinterpret the mentioned group theoretic theorems graph theoretically. This leads to many new questions some of which are solved and others are widely open.

Math Colloquium

### Speaker: Rögnvaldur Möller

Title: Infinite cubic vertex-transitive graphs

Location: Naustið, Endurmenntun (here)

Time: Thursday, May 21, at 15:00-16:00.

### Abstract:

Tutte’s two papers from 1947 and 1959 on cubic graphs were the starting point of the in-depth study of the interplay between the structure of a group and the structure of a graph that the group acts on. In this talk I will describe applications of Tutte’s ideas where it is assumed that the graph is infinite and the stabilizers of vertices are infinite.