Young Mathematicians Get To Know the Professional World

Ecosystems are made up of animate and inanimate components whose populations form a community. But what laws determine the dynamics of these fascinating systems? And how do predator and prey species interact with each other?

Simualtion of Populations

In this project, the students consider mathematical models to describe the development of populations. Starting with intuitive growth models of a species through to the interactions of a predator-prey relationship, they try to describe and understand the relationships and simulate them on the computer.

The group is supervised by our colleague Tim Nicolai from the division »Mathematics for Vehicle Engineering« at the Fraunhofer ITWM.

You can find more information on our division »Mathematics for Vehicle Engineering« here.

In this project, the participants deal with a fictitious scenario in the year 2030. A group of young mathematicians at University of Kaiserslautern-Landau is analyzing the consequences of a new, unknown virus that is causing an increase in cases of illness following a science conference. While virologists work on identifying the virus and its transmission, the group develops a mathematical model to answer key questions:

• Will there be a major outbreak?
• When Will the Number of Cases Decline Again?
• What Measures Help to Contain the Virus?
• Which Variant of the New Virus Will Prevail?

The group is supervised by Marvin Schulte from the department »Transport Processes« and from the »Technomathematics« working group in the department  »Mathematics« at University of Kaiserslautern-Landau in Kaiserslautern.

Our institute has worked intensively on this research focus, especially during the coronavirus pandemic. More about our work here.

Sorting out defective products plays an important role in industrial production. The inspection should be as robust, fast and objective as possible. Automatic inspection systems offer a promising alternative to manual inspection.

Synthetic Images for Defect Analysis

But how can an algorithm decide whether the product is defective? This requires many examples of defective and defect-free products. Since collecting real data is expensive and time-consuming, synthetic images are used. For this purpose, it is necessary to model the possible defects that may occur.

In this project we ask ourselves the following questions:

• What Properties Can Be Used to Describe Cracks and How Can They Be Used to Develop a Mathematical Model?
• How Do You Assess Whether the Model Is Useful? How Do You Compare Different Mathematical Models for the Same Question?

The aim is to model realistic scratches based on real data and to select the model parameters in such a way that they correspond to the scratch properties.

The group is supervised by Natascha Jeziorski from the »Image Processing« department at the Fraunhofer ITWM.

Our project »DAnoBI« is an example of our institute's work in this research area. 

Prime numbers are the basic building blocks of integers. Everyone knows them, they have applications everywhere: from gears to fractions to encryption – and they still raise many questions.

In this project we will deal with many properties of prime numbers, starting with finding them in the first place. The normal methods no longer work if we want prime numbers with 100 or even 1000 digits. On October 23, 2024, Spiegel reported: »Amateur mathematician from the USA discovers largest known prime number.« We want to clarify how this works and how this discovery should be classified.

This goes hand in hand with the question of how many prime numbers there are and how rare they are. Depending on your interests, we can also look at applications of prime numbers, for example in cryptography.

The group is led by Prof. Dr. Claus Fieker and Prof. Dr. Max Horn from the »Algebraic Geometry« working group in the »Mathematics« department at University of Kaiserslautern-Landau.

You can find more information about the department »Mathematics« at University of Kaiserslautern-Landau here.