Geometry and Topology at the Department of Mathematics, University of Oslo

Emphasized Research Area

The Faculty of Mathematics and Natural Sciences at the University of Oslo has selected the research group in Geometry and Topology at the Department of Mathematics as an emphasized research area, or more specifically as an "emerging top-tier research group". This emphasis is the joint responsibility of the Faculty and the Department. The leader for the Geometry/Topology group is Professor John Rognes.

Theme

A large part of the group's research concentrates on algebraic topology and algebraic K-theory, with applications to geometric topology.

We study structured ring spectra, which represent multiplicative cohomology theories, but considered as "brave new rings". In particular we are interested in viewing these ring spectra as generalized rings of functions on new geometric objects. In this way we wish to systematically understand invariants of these new geometries, such as their algebraic K-theory, their differential geometry, etc. One goal is to use this geometric perspective to explain the structure of the algebraic K-theory of group rings over the sphere spectrum, which in turn explains much of what we know about automorphisms of high-dimensional manifolds. The methods presently used for this study include topological cyclic homology, topological Hochschild homology, topological André-Quillen homology and topological logarithmic structures.

The group is also involved in relating homotopy theory at large to other subjects. Motivic homotopy theory is an in vogue example of a homotopy theory that arises in algebraic geometry. An emerging example is a new homotopy theory of C*-algebras.

Participants

Tenured faculty at the Department of Mathematics:
Hans Brodersen, Bjørn Jahren, Paul Arne Østvær, John Rognes.
PhD students:
Knut Berg (w/ Rognes and Jahren), Vegard Fjellbo (w/ Rognes and Østvær), Nikolai Bjørnestøl Hansen (w/ Brodersen and Jahren).
Master students:
Eivind Dahl (w/ Rognes), Stener Nerland (w/ Jahren).

Research guests

Earlier Participants

Tenured faculty:
Per Holm, Jon Reed, Per Tomter.
Guest professors:
Andy Baker (Glasgow), Marcel Bökstedt (Århus), Bob Bruner (Wayne State University).
Guest researchers:
Helmer Aslaksen, Holger Reich, Philipp Reinhard, Birgit Richter.
Postdoctoral fellows:
Clark Barwick, Halvard Fausk, Thomas Kragh, Sverre Lunøe-Nielsen, Steffen Sagave, Christian Schlichtkrull, Markus Spitzweck, Andreas Holmstrøm.
PhD students:
Peter Arndt (w/ Spitzweck),

Candidates with completed degrees

Seminars

Conferences

Projects and Networks

Earlier Activities

John Rognes / October 24th 2014