Operator Algebras: structure and classification of
and von Neumann Algebras, especially those coming from groups and their
actions on spaces (metric spaces, probability measure spaces);
rigidity aspects in von Neumann algebras (W*-rigidity)
Subfactor Theory: analysis
subfactors of finite Jones index, combinatorics of standard invariants,
relations to Algebraic Quantum Field Theory and Conformal Field Theory.
Ergodic Theory: actions of groups
by measure preserving
their classification up to orbit equivalence, invariants (such as cost,
L2-Betti numbers, etc), related rigidity aspects (such as orbit
equivalence and cocycle superrigidity, etc).
Group Theory: L2 invariants,
rigidity properties, approximation properties, aspects of geometric
group theory, etc