## Seminar Talks

List of seminar talks (pdf) since 1999.

#### Vortrag Habilitationswerberin

**Title:**Cluster growth models and fractals

**Speaker:**Dr. Ecaterina Sava-Huss (TU Graz)

**Date:**Donnerstag, 14.2.2019, 11:00 s.t.

**Room:**Seminarraum AE06, Steyrergasse 30, EG

**Abstract:**

A significant part of my research deals with understanding the behavior of the following cluster growth models: internal diffusion limited aggregation, the rotor model, and the divisible sandpile model.

These models can be run on any infinite state space, and they are based on particles moving around according to some rule (that can be either random or deterministic) and aggregating. Describing the limit shape of the cluster whjich these particles produce is one of the main questions one would like to answer. For some of the models, the limit shape is hard to understand, and according to simulations, the fractal nature of the sets they produce is, from the mathematical point of view, far away from being understood. I will present several results concerning the limit shape of the clusters. In particular, I will present a limit shape universality result on the Sierpinski gasket graph, and conclude with some future research directions one can pursue within this topic.

#### Strukturtheorie-Seminar (Master-Vortrag)

**Title:**The Wiener index of Schreier graphs of the basilica automaton

**Speaker:**Stefan Hammer (TU Graz)

**Date:**7.2.2019, 11:00 s.t.

**Room:**Seminar room AE02, Steyrergasse 30, ground floor

**Abstract:**

Automata and graphs are associated in many ways. For invertible automata one can

define the automaton group and observe its action on the set of finite words over the

input alphabet. This leads to the construction of Schreier graphs.

The sum of all distances in a graph, called Wiener index, is a graph property of wide interest. Harry Wiener showed that the properties of molecules are related to the Wiener index of chemical structural formulas. In my presentation I am going to introduce all necessary tools and prove an upper bound for the Wiener index of Schreier graphs of the Basilica automaton.

#### Workshop

**Title:**Groups, Automata and Graphs

**Speaker:**https://www.math.tugraz.at/GAG/ ()

**Date:**February 11-12, 2019

**Room:**Seminarroom AE06

**Abstract:**

More information concerning the talks and the speakers can be found on the webpage: https://www.math.tugraz.at/GAG/

If you want to attend the workshop, please let us know in order to organize the coffee breaks.