### Talks in 2019

#### 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:**Workshop: East Austria TDA Meeting

**Speaker:**()

**Date:**30.01.2019

**Room:**Seminarraum 2 Geometrie

**Abstract:**

Schedule:

9:30-10:00 Coffee

10:00-10:50: Michael Kerber: Algorithmic advances for multi-parameter persistence

10:50-11:10: Coffee

11:10-12:00: Mickael Buchet: On the structure of indecomposable modules of multi-dimensional commutative grids

12:00-12:30: Arnur Nigmetov: Metric spaces with expensive distances

12:30-14:00: Lunch break

14:00-14:50: Hubert Wagner: Bregman geometry and Information Topology

14:50-15:20: Hannah Schreiber: Discrete Morse Theory for Computing Zigzag Persistence

15:20-15:50: Coffee

15:50-16:40: Herbert Edelsbrunner: Tri-partitions of complexes

16:40-17:30: Georg Osang: Persistence of Multi-Covers

17:30- Discussions

#### 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.

#### Vortrag

**Title:**Japanese employment system

**Speaker:**Prof. Dr. Hisashi Okamoto (Kobe Gakuin University (Japan))

**Date:**Freitag, 25. 1. 2019, 14:00 c.t.

**Room:**Seminarraum Analysis-Zahlentheorie (NT02008), Kopernikusgasse 24/II

**Abstract:**

The so-called Japanese employment system consists of three unique components: long-term employment, seniority-based wage system and enterprise unions. Partly because the system worked properly, Japan successfully achieved the rapid growth in 1960s.

In the talk, first, we give a brief description of Japanese employment system. Then, we introduce two leading theories explaining the economic rationality of seniority-based wage system. Finally, we show an application of such theories as these to empirical analysis taking one of my studies as an example.The details are as follows.

1. An overview of Japanese employment system

Japanese employment system

has three unique components such as

Long-term employment

Seniority-based wages system

Enterprise unions

worked well especially in 1960s, but has been working poorly since early 1990s ,when the bubble economy collapsed

is undergoing the drastic reform affected by the progress in the reform in corporate governance

2. Focus on seniority-based wage system

There exist two leading theories explaining the rationality of seniority-based wage system as below

Human capital theory ( by G. Becker )

Delayed compensation theory ( by P. Lazear )

The former sheds light on the role of the system in employees’ skill formation, and the latter regards it as an incentive device

In Japan, delayed compensation theory seems more plausible

3. An application of economic theories to empirical analysis

We show how economic theories are applied to empirical analysis taking one of my studies as an example which employed the theories explained above for examining “Employment Ice Age” (the period just after the bubble economy collapsed, when Japanese firms seriously cut back on hiring of new university graduates influenced by negative macroeconomic shocks)

#### Zahlentheoretisches Kolloquium

**Title:**Diophantine approximation with primes from imaginary quadratic number fields

**Speaker:**Marc Technau (TU Graz)

**Date:**11.1.2019, 14:15

**Room:**Seminarraum Analysis und Zahlentheorie

**Abstract:**

A classical variation of Dirichlet's theorem on Diophantine approximation asks for how well a given number $\alpha\in\mathbb{R}\setminus\mathbb{Q}$ can be approximated by fractions with prime denominators. This problem has attracted the attention of a number of researchers, amongst these, Vinogradov, Vaughan, Harman, Jia, and Heath-Brown. Ten years ago, Matomäki achieved unconditionally the result that, for any $\epsilon>0$, there are infinitely many primes $p$ such that $\min_{a\in\mathbb{Z}} \lvert p\alpha-a \rvert < p^{-1/3+\epsilon}$.---A result previously known only on assuming the Generalised Riemann Hypothesis.

In this talk we consider a natural two-dimensional variation of the aforementioned problem. Namely, for an imaginary quadratic number field $\mathbb{K}\subset\mathbb{C}$ and $\alpha\in\mathbb{C}\setminus\mathbb{K}$, we seek to establish the existence of infinitely many prime elements $p$ in the ring of algebraic integers $\mathcal{O}$ of $\mathbb{K}$ such that $p\alpha$ is `close' to some element of $\mathcal{O}$ in a manner to be made precise in the talk.

The main ingredients of our attack on the problem are a smoothed version of a sieve method due to Harman, Poisson summation, and some point distribution results in the setting of $\mathcal{O}$ in the spirit of Vinogradov. In particular, the introduction of smoothing allows for stronger results than those based on truncating certain Fourier series. For technical reasons we only obtain results for those $\mathbb{K}$ with class number one.

The talk is based on joint work in progress with Stephan Baier.}

#### Vortrag im Seminar für Kombinatorik und Optimierung

**Title:**Restricted Assignment Scheduling with Resource Constraints

**Speaker:**Hans Kellerer (Institut für Statistik und Operations Research, Universität Graz)

**Date:**8.1. 2019, 14:15

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

**Abstract:**

We consider parallel machine scheduling with job assignment restrictions,

i.e., each job can only be processed on a certain subset of the machines.

Moreover, each job requires a set of renewable resources. Any resource can

be used by only one job at any time. The objective is to minimize the

makespan. We present approximation algorithms with constant worst-case bound

in the case that each job requires only a fixed number of resources. For

some special cases optimal algorithms with polynomial running time are

given. If any job requires at most one resource and the number of machines

is fixed, we give a PTAS. On the other hand we prove that the problem is

APX-hard, even when there are just three machines and the input is

restricted to unit-time jobs.