Geometry & Topology
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.
Lots of dots: Homology counts the circles that you see.
An open-closed cobordism.
Homological stability for the symmetric groups in a spectral sequence.
Petter Andreas Bergh, Gustavo Jasso and Marius Thaule
Higher n-angulations from local rings
Journal of the London Mathematical Society
Nils Andreas Baas, NC Seeman and Andrew Stacey
Synthesising topological links
Journal of Mathematical Chemistry
Nils Andreas Baas
Higher order architecture of collections of objects
International Journal of General Systems
Michael J. Hopkins and Gereon Quick
Hodge filtered complex bordism
Journal of Topology
Ehud Meir and Markus Szymik
Drinfeld centers for bicategories
Existence of rational points as a homotopy limit problem
Journal of Pure and Applied Algebra
Commutative S-algebras of prime characteristics and applications to unoriented bordism
Algebraic and Geometric Topology
Homotopies and the universal fixed point property