Department of Mathematical Sciences

Geometry & Topology

Second order Brunnian ring. Figure.

Our research in geometry and topology spans problems ranging from fundamental curiosity-driven research on the structure of abstract spaces to computational methods for a broad range of practical issues such as the analysis of the shapes of big data sets.

The members of the group are all embedded into a network of international contacts and collaborations, aim to produce science and scientists of the highest international standards, and also contribute to the education of future teachers.


About Geometry and Topology

Geometry has always been tied closely to mathematical physics via the theory of differential equations. It uses curvature to distinguish straight lines from circles, and measures symmetries of spaces in terms of Lie groups, named after the famous Norwegian mathematician Sophus Lie.

Topology, in contrast, is the study of qualitative properties of spaces that are preserved under continuous deformations. The spaces in question can be tame like a smooth manifold, or wild and hard as rock.

Topological ideas arise in practical problems, and research in topology still finds new applications, in particular to mathematical problems that are not directly phrased in terms of numbers and functions.

Homotopy theory (a subdiscipline of topology) has many applications within mathematics itself, in particular to algebra and number theory.

  • Figur som illustrerer anvendelse av homotopi.

    Lots of dots: Homology counts the circles that you see.

  • An open-closed cobordism. Figure.

    An open-closed cobordism.

  • Matrix of symmetric groups. Figure.

    Homological stability for the symmetric groups in a spectral sequence.


Research projects

Gereon Quick and Markus Szymik collaborate in Motivic Hopf equations, a project supported by the Research Council of Norway.

Recent Publications

Emilie Bjørlo Arentz-Hansen, Petter Andreas Bergh and Marius Thaule
The morphism axiom for n-angulated categories
Theory and Applications of Categories

Petter Andreas Bergh, Gustavo Jasso and Marius Thaule
Higher n-angulations from local rings
Journal of the London Mathematical Society

Elena Celledoni, Markus Eslitzbichler and Alexander Schmeding
Shape analysis on Lie groups with application in computer animation
Journal of Geometric Mechanics (JGM)

Daniel G. Davis and Gereon Quick
Profinite and discrete G-spectra and iterated homotopy fixed points
Algebraic and Geometric Topology

Alexander Schmeding and Christoph Wockel
Functorial aspects of the reconstruction of Lie groupoids from their bisections
Journal of the Australian Mathematical Society

Alexander Schmeding and Geir Bogfjellmo
The tame Butcher group
Journal of Lie theory

Alexander Schmeding, Geir Bogfjellmo and Rafael Dahmen
Character groups of Hopf algebras as infinite-dimensional Lie groups
Annales de l'Institut Fourier

Alexander Schmeding and Christoph Wockel
(Re)constructing Lie groupoids from their bisections and applications to prequantisation
Differential geometry and its applications (Print)

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