Geometry and Topology at the Department of Mathematics,
University of Oslo
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 toptier 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 Ktheory, 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
Ktheory, their differential geometry, etc. One goal is to use this
geometric perspective to explain the structure of the algebraic Ktheory
of group rings over the sphere spectrum, which in turn explains much
of what we know about automorphisms of highdimensional manifolds. The
methods presently used for this study include topological cyclic homology,
topological Hochschild homology, topological AndréQuillen 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.
 Tenured faculty at the Department of Mathematics:

Hans Brodersen,
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),
Jonas Irgens Kylling
(w/ Østvær and Rognes).
 Master students:

Håkon Andreas Kolderup
(w/ Østvær),
Stener Nerland (w/ Jahren).
Research guests
 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 LunøeNielsen,
Steffen Sagave,
Christian Schlichtkrull,
Markus Spitzweck,
Andreas Holmstrøm.
 PhD students:

Peter Arndt
(w/ Spitzweck),
Candidates with completed degrees
John Rognes / February 4th 2016