## Seminar Talks

List of seminar talks (pdf) since 1999.

#### Strukturtheorie-Seminar

**Title:**Central Limit Theorem for the capacity of the range of stable random walks

**Speaker:**Dr. Stjepan Šebek (Univ. Zagreb)

**Date:**Thursday, 25. April 2019, 15:15

**Room:**Seminar room A306, Steyrerg. 30/3

**Abstract:**

In this talk, we will establish a central limit theorem for the capacity of

the range process for a class of d-dimensional symmetric alpha-stable random

walks with the index satisfying $d \geq 3\alpha$. Our approach is based on

controlling the limit behavior of the variance of the capacity of the range

process which then allows us to apply the Lindeberg-Feller theorem.

#### Strukturtheorie-Seminar

**Title:**Jacobi Polynomials and the Discrete Laguerre Operator

**Speaker:**Aleksey Kostenko (Univerza v Ljubljani / Universität Wien)

**Date:**28.3.2019, 14:00 c.t.

**Room:**SR AE02, Steyrergasse 30, ground floor

**Abstract:**

The talk is focused on Bernstein-type estimates for Jacobi polynomials and their applications to various branches in mathematics. This is an old topic but we want to add a new wrinkle by establishing some intriguing connections with dispersive estimates for a certain class of Schrödinger equations whose Hamiltonian is given by the generalized Laguerre operator, i.e., the Jacobi matrix associated with generalized Laguerre polynomials. These operators feature prominently in the recent study of nonlinear waves in (2+1)-dimensional noncommutative scalar field theory since they appear as the linear part in the nonlinear Klein--Gordon and the nonlinear Schrödinger equations investigated in the recent of Chen, Fröhlich and Walcher (2003) and Krueger and Soffer (2015), respectively.

We show that dispersive estimates for the evolution group are connected with Bernstein-type inequalities for Jacobi polynomials. We use known uniform estimates for Jacobi polynomials to establish some new dispersive estimates. In turn, the optimal dispersive decay estimates lead to new Bernstein-type inequalities.

The talk is based on joint work with T. H. Koornwinder (Amsterdam) and G. Teschl (Vienna).

#### 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.