Are you interested in pure mathematics? Do you enjoy analytical thinking and rigorous proof writing? Do you want to dive deep into some topic? Then you may want to consider writing your thesis in our group! Please contact us to find out about current opportunities. Below is some general information on what to expect, along with some potential topics.
Perhaps one of the most important things comes right at the start, namely finding a suitable topic. Being able to focus on something for several months and acquiring expert-knowledge is a unique opportunity, so it should be something which genuinely interests you, and of course lies within our area of expertise.
In general, it will be some research direction of discrete mathematics, potentially with connections to other areas like algebra, number theory, probability, or theoretical computer science.
The focus is on rigorous mathematical theory building (definitions, theorems, proofs), but the thesis may of course also contain some more practical elements, such as motivation for / applications of the research topic, implementations of algorithms, and/or experimental evidence.
Combinatorial designs are mathematical objects with a lot of symmetry. One important class of such designs are Steiner systems, which one can loosely think of as high-dimensional equi-partitions. For those to exist, some divisibility conditions have to be satisfied. The question of whether these conditions are also sufficient has intrigued mathematicians for a long time, until 2014.
Hamilton cycles are one of the most intensively studied objects in graph theory, with connections to many other areas. Recently, a long-standing problem on their existence in so-called expander graphs has been solved.
Svatopluk Poljak was a Czech mathematician who made important contributions to discrete mathematics and combinatorial optimization.
Yes, we expect your thesis will be written in English.
There is no fixed length. Usually, a bachelor's thesis is expected to lie at around 25-50 pages and a Master's thesis around 60-90 pages.
No way! Your thesis should be typeset in LaTeX.
You're more than welcome to. In fact, we strongly encourage you to bring in your own ideas. However, the final topic should lie within our area of expertise, so some adjustments might be necessary.
That depends a lot on you. We are always happy to discuss any issues and provide guidance. However, you should be well prepared when you come to the meetings.
arXiv (pronounced as "archive") is an online platform for sharing preprints of research papers immediately with the research community. It is not peer-reviewed, so if a paper is already published, you should always cite the journal version.
