Discrete Mathematics

Combinatorics

Istvan Tomon 

Topic areas for bachelor or master theses:

• Extremal graph theory
• Ramsey theory
• Combinatorial geometry
• Linear algebraic methods in combinatorics

Example of possible thesis projects:

• Finding regular subgraphs (Erdos-Sauer problem)
• Ramsey theory of structured graph families (Erdos-Hajnal conjecture)
• Finding large convex sets among points in general position (Erdos-Szekeres conjecture) and higher dimensional variants
• Coloring geometric graphs
• The Cap set problem and the slice-rank method
• Non-vanishing linear maps (Alon-Jaeger-Tarsi conjecture) and hyperplane covers
   

This list showcases various topics in combinatorics with recent developments that I am interested in, and is not complete. I am open to negotiating several other projects as well. The only prerequisite is basic understanding of graph theory, combinatorics, and linear algebra.

Istvan Tomon Associate professor

Email

+46 90 786 56 71

Graph theory, discrete probability, extremal combinatorics

Victor Falgas Ravry

I can supervise theses at all levels on the following topics:

• Random graphs, random graph models, percolation theory
• Extremal graph theory, extremal problems for graphs, hypergraphs and set systems
• Combinatorial games, especially games on graphs
• Graph processes and graph automata such as bootstrap percolation or the spread of a virus through a network
• Combinatorial number theory
• All aspects of graph theory
• amongst others

Extremal and probabilistic combinatorics, my domain of expertise, is a highly active area of research, with many exciting developments just in the last few years. I thus always have at hand a dozen or so possible projects linked to recent advances and results. If you are interested in writing a thesis under my supervision, just send me an email or knock on my office door to arrange a meeting. We can then discuss your mathematical background and interests before I suggest 3-4 possible thesis topics.

Victor Falgas Ravry Associate professor

Email

+46 90 786 78 02

Graph theory, hypergraphs, and computational combinatorics

Klas Markström

I can supervise  projects which connect directly to my own research or belong to the general areas of mathematics in which I work.

Some examples:

• Graph theoretical problems of different kinds
• Hyperraphs and design theory
• Problems in probabilitity theoy and random graphs
• Mathematical physics, either with connections to statistical mechanics or quantum computing
• Algorithms and complexity theory
• The theory of combinatorial games. This includes both underlying theory and algorithms

Klas Markström Professor

Email

+46 90 786 97 21

Discrete geometry, coding theory and cryptography

Klara Stokes

Topic areas for bachelor thesis

• Geometry, in particular geometric combinatorics and projective geometry over finite fields.
• Combinatorics, in particular graphs and other combinatorial objects such as hypergraphs, simplicial complexes, incidence geometries, matroids and designs.
• Algebraic tools in geometry and combinatorics.
• Group theory, in particular symmetry groups acting on discrete and/or geometric objects.
• Coding theory, cryptography, and other applications to computer science.

Klara Stokes Associate professor

Email

+46 90 786 55 92

Discrete mathematics

Lars-Daniel Öhman

Topic areas for bachelor theses:

• Graph theory
• Design theory
• History and philosophy of mathematics
• Axiomatic basis of mathematics

Example of possible thesis projects:

• Writing an exposition of the Bruck-Ryser-Chowla theorem, with expanded definitions and explanations, and carefully worked examples
• Writing a survey on progress in the open problem of the existence of biplanes
• Generating complete lists of small combinatorial designs using computer programming

Lars-Daniel Öhman Associate professor, research fellow

Email

+46 90 786 59 36

Representation theory and number theory

Henrik Gustafsson

Topic area suggestions for a BSc or MSc thesis:

• Computing with nilpotent orbits in classical Lie algebras
• Integration with p-adic numbers. For a fun introduction to p-adic numbers, see: https://youtu.be/3gyHKCDq1YA
• Survey of the classification of Lie algebras and Lie groups
• How lattice models from statistical mechanics describe special functions in representation theory
• Representations of the general linear group, Young tableaux and Kashiwara crystals
• Fourier coefficients of automorphic forms
• Solvable lattice models and quantum groups

Many of the projects are suitable for a mixture of smaller research problems and a survey of existing literature depending on thesis-level and preference.

Henrik Gustafsson Assistant professor

Email

+46 90 786 77 55