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

Emphasized Research Area

In the period 2007-2012, the Faculty of Mathematics and Natural Sciences at the University of Oslo 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".

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, Kim Frøyshov, Paul Arne Østvær, John Rognes.
Professor II:
Robert R. Bruner, Ivan Panin, Oliver Röndigs.
Postdocs:
Charanya Ravi, Glen Wilson.
PhD students:
Vegard Fjellbo (w/ Rognes and Østvær), Nikolai Bjørnestøl Hansen (w/ Brodersen and Jahren), Alice Hedenlund (w/ Rognes and Østvær), Gard Helle (w/ Frøyshov and Rognes), Håkon Andreas Kolderup (w/ Østvær and Rognes), Jonas Irgens Kylling (w/ Østvær and Rognes), Sabrina Pauli (w Østvær and Wickelgren).
Master students:
Niels Bonten (w/ Rognes), Stener Nerland (w/ Jahren), Tony Valle (w/ Frøyshov).

Research guests

Earlier Participants

Tenured faculty:
Bjørn Jahren.
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), Knut Berg (w/ Rognes and Jahren).

Candidates with completed degrees

Seminars

Conferences

Projects and Networks

Nearby Departments

Earlier Activities

John Rognes / October 24th 2017