NTNU Trondheim, Norway
Marius
Thaule.
Head of Department
Department of Mathematical Sciences, NTNU
Higher dimensional triangulated categories · Axiom (N4)
The higher octahedral axiom
The axioms for n-angulated categoriesThe morphism axiom for n-angulated categories
Topological data analysis · Figure 5
One winding. A clearer feature.
Circular coordinates before and after reducing the cocycle’s winding number from 23 to 1.
Lifting cocycles: From heuristic to theory
Higher dimensional triangulated categories · Theorem 4.9
Three definitions. One bracket.
In a pre-n-angulated category, the three Toda brackets coincide when consecutive morphisms compose to zero.
Toda brackets in n-angulated categories · 2023
Cobordism categories · Figure 1
Between open and closed strings.
An open-closed cobordism: a surface relating interval and circle boundaries.
On open and closed strings · 2016
Topological data analysis · Figure 2
A lift that works.
The unscaled lift fails the cocycle condition. Scaling by 2 yields an integral cocycle and valid circular coordinates.
Lifting cocycles: From heuristic to theory
About.
I am Head of the Department of Mathematical Sciences at the Norwegian University of Science and Technology (NTNU).
I specialize in algebraic topology and belong to the Geometry & Topology group . My research spans higher dimensional triangulated categories, stable homotopy theory, cobordism categories, and topological data analysis.
02 / Research
Research.
Higher dimensional triangulated categories, stable homotopy theory, cobordism categories, and topological data analysis.
Papers
2013–2025Lifting cocycles: From heuristic to theory
arXiv:2509.16102 · Submitted 19 September 2025
Toda brackets in n-angulated categories
arXiv:2312.13209 · Submitted 20 December 2023
On open and closed strings
Mathematica Scandinavica 119 (2), 223–236
The morphism axiom for n-angulated categories
Theory and Applications of Categories 31 (18), 477–483
Higher n-angulations from local rings
Journal of the London Mathematical Society 93 (1), 123–142
The Grothendieck group of an n-angulated category
Journal of Pure and Applied Algebra 218 (2), 354–366
The axioms for n-angulated categories
Algebraic & Geometric Topology 13 (4), 2405–2428
03 / Teaching
Teaching.
See the course archive for courses I have taught at NTNU.
See this website for student projects I have supervised.
Course archive
Interested in a thesis or project?
My research interests are a good starting point. Get in touch to discuss possible topics.
Discuss a project04 / Academic service
Academic
service.
I am a board member of the Norwegian Mathematical Association .
I serve as a referee for multiple journals.
Conference organization
2013–2025Abel Symposium · Stable Homotopy Theory
Trondheim · 23–27 June 2025
Abel Symposium
Geiranger · 4–8 June 2018
Topology and Applications
NTNU · 30 November–2 December 2016
Geometry and Lie Theory
NTNU · 3–4 November 2016
Nordic Topology Meeting
NTNU · 27–28 November 2014
Homological Methods in Algebra
Lund · 10–11 June 2013
06 / Contact
Get in touch.
Write
Department of Mathematical Sciences
NTNU, N-7491 Trondheim
Norway