Projects and Research Group

Current members

• Cyril Matoušek (PhD student, Aarhus University)

Former members

Former PhD students

• Dave Murphy (defended 2023, University of Glasgow)

• Damian Wierzbicki (defended 2022, University of Glasgow)

Former postdocs

• Charley Cummings (postdoc, 2022-2026, Aarhus University)

• Davide Morigi (postdoc, 2022-2025, Aarhus University)

This project is funded by the Villum Young Investigator Programme of THE VELUX FOUNDATIONS.

Cluster algebras and their combinatorics have emerged as an important feature throughout mathematics. The project addresses the fundamental question: How can we formally compare their various guises? We will exploit the answer to both advance our understanding of cluster algebras and for explicit computation of important examples from geometry and topology.

This project will be funded as a DFF-Research Project1 by Danmarks Frie Forskningsfond.

In the 1930s, Øystein Ore proved that a finite group is cyclic if and only if its lattice of subgroups is distributive. The project aims to establish an analogous programme for triangulated categories: it will show that distributivity of the lattice of thick subcategories of a triangulated category has strong implications both for the properties of the triangulated category itself and for the algebraic and geometric objects that underlie it.