Amenability of Thompson’s group F
Can Thompson’s group F admit an average that is unchanged by every group translation?
Groups and operators
Structure in groups, representations and infinite-dimensional spaces.
Subjects: Algebra and geometry · Analysis and dynamics · Topology
Problems in this collection
7 problemsBaum–Connes conjecture
Can the proper-action geometry of a countable discrete group recover the K-theory of its reduced operator algebra?
Kaplansky’s zero-divisor conjecture
Can two nonzero finite algebraic combinations of elements of a torsion-free group multiply to zero?
Invariant subspace problem
Must every bounded linear operator on complex Hilbert space preserve a nontrivial closed subspace?
UCT problem for nuclear C*-algebras
Does every separable nuclear C*-algebra satisfy the universal coefficient theorem relating its K-theoretic invariants?
Cherlin–Zilber algebraicity conjecture
Must every infinite simple group with finite logical dimension come from algebraic geometry?
Mazur’s separable quotient problem
Can every infinite-dimensional Banach space be collapsed to an infinite-dimensional space described by a countable dense set?