Junior research group "Non-commutative geometry"
Mentors
Detlev Buchholz, Ralf Meyer, Karl-Henning Rehren, Thomas
Schick
Research goals are in particular
von Neumann algebras (their
rigidity -as pioneered by Popa,
the free factor problem, L2-Betti numbers), applications to number theory (like
spectral interpretations of zeros of L-functions), applications to
representation theory (sheaves on buildings, Hecke algebras of reductive p-adic
groups), isomorphism conjectures.
Methods include
the rigidification/categorification of homological
aspects, sheaf theory on buildings, development of analytic aspects of
homological algebra (e.g. of Schwartz spaces), geometric group theory, advanced
algebraic geometry and topology.
Coordinator: Thomas
Schick