Two Bachelor's Degree Project Presentations in Mathematics: Carl Kjellander and Olle Nilsson

Carl Kjellander

Time: 13:15-14:00

Place: 101130

Title: The Temperley-Lieb algebra and cellular algebras

Abstract: We introduce the Temperley-Lieb algebra with generators and relations. We then give the diagrammatic interpretation of it and prove they are isomorphic. After this we give an introduction to cellular algebras, prove the Temperley-Lieb algebra is cellular using half diagrams, and give a criterion for semi-simplicity.

Olle Nilsson

Time: 14:15-15:00

Place: 101130

Title: Usage of Markov chains as graph theory for mathematical analysis of football

Abstract: In this thesis, we will be exploring how we can use Markov chains as a method to construct a graph from Hammarby's women's football team's games season 2024/2025. This graph will be explored using tools for graphs from the book Newmans bok about networks. We study twelve graph-theoretic metrics, and these metrics will measure different aspects of the team and players' passing structures.

These metrics are grouped into Centrality, Bridge and Similarity measures. Centrality, how central a player is to the passing structure. Bridges, how well the team manages to bridge the gap between the different blocks, such as defenders, midfielders and strikers and if there are players who play as bridge players, which makes these gaps smaller. Likeness, how similar different players are in their decisions and if there exist pairs of players who pass more to each other rather than to the rest of the team. We will see that these groups of metrics are precisely the groups in which we can create a model to evaluate these aspects of football better with a machine learning model.

We will also see that when it comes to passing structure, the most important players for Hammarby are the defenders, who are most involved in the passing structure and the build-up play. This is due to Alice Carlsson, who is a defender and is the most valuable player when it comes to build-up play for Hammarby based on these metrics. We will also see that the midfielders as a group will be important, as the midfielders as a group have a similar score as the defenders in a group. If we exclude Carlsson, the midfielders are equally important in some metrics.