The project addresses two distinct, yet interconnected work packages.
1) Curtis-Tits groups
This work package falls within the realm of algebra, more precisely group theory. This is broadly speaking the study of symmetry of certain geometric and combinatorial objects. Curtis-Tits groups are generalizations of a class of groups of relevance to Theoretical Physics called Kac-Moody groups. Generally such groups are in some sense infinite dimensional.
The purpose of the project is to completely classify and describe these groups In terms of a compact finite set of data and to study these groups and related geometric and combinatorial structures in terms of this data.
We also wish to explore applications in various areas of mathematics and computer science.
2) Mathematical Research and Teaching with Proof Assistants
The purpose of this work package was to address the well-known difficulties that students encounter when learning to write structured proofs, i.e. rigorous explanations of mathematical ore more generally formal logical statements.
There exist many useful software packages for teaching and assessing computational aspects of mathematics. However, one of the major obstacles in teaching conceptual understanding and critical thinking skills within mathematics and sciences in general the fact that it is hard to produce and assess sufficient numbers of practice problems.
There are so-called proof assistants, but these have been developed mainly for advanced computer science purposes and are unsuitable for students without advanced understanding of modern programming languages.
Notably in the current computer age, computational skills are increasingly becoming irrelevant, whereas transferable skills coming from conceptual understanding are increasingly important.
