Title: Moessners Sats

Linus Santesson Råsten(Bachelor Thesis)

Time: Tuesday 12. Dec 2023, 10:00-11:00

Place: Mittag-Leffler Room (Albano, SU)

Supervisor: Håkan Granath

Abstract: In this essay, we will cover what is known as Moessner’s Theorem, which was written in 1951 by the German mathematician Alfred Moessner. The theorem is based in, and builds upon, a characteristic of the natural numbers where adding them together in a certain way will always result in even squares. Since the finding of Moessner’s Theorem, various other mathematicians have studied and added to the process therein and found additional properties of it. In the following text, we will explore the theorem and move on to first partially proving it through an inductive proof. Following this we will also look closer at, and flesh out, a complete proof using graph theory.

Title: Convolution on compact groups and natural language processing

Mbwenga Maliti (Bachelor Thesis)

Time: Tuesday 12. Dec 2023, 1:30-2:30

Place: Cramér -room (Albano, SU)

Supervisor: Rikard Bøgvad

Abstract: There is a mathematical framework that can be used for explicitly constructing neural networks with internal representations of its input that are equivariant to the action of an arbitrarily chosen compact group. I have described parts of it and used a simple model of languages and translations to examine a part of the aforementioned framework necessary for applying it to natural language processing. There is a significant amount of work remaining in order to build a full neural network according to the mathematical framework, as well as in order to incorporate more sophisticated models of language and translations into it.

See all presentations during week 50 here:

Thesis presentations (PDF) (118 Kb)