clopen.solutions

Open problems

980 registered problems.

OP-00070 Open
An explicit rational Valiant-rigid matrix family
CO · circuit lower bounds · matrix rigidity · OpenProblemsInNLA
OP-00262 Solution claimed
Infinitesimal rigidity detects unique size-two factors in the presence of zeros
NA · infinitesimal rigidity · OpenProblemsInNLA · positive semidefinite factorizations · positive semidefinite rank
OP-00512 Open
A strictly convex function on every simple manifold
DG · AIM Open Applied Problems · boundary rigidity · simple manifolds · strictly convex functions
OP-00541 Open
Lens rigidity for nontrapping surfaces with conjugate points
DG · AIM Open Applied Problems · conjugate points · lens rigidity · scattering relations
OP-00556 Open
Boundary rigidity of simple manifolds in dimensions at least three
DG · AIM Open Applied Problems · boundary rigidity · simple manifolds · travel-time tomography
OP-00561 Open
Existence of a flexible closed C² surface in three-space
DG · AIM Open Applied Problems · flexible surfaces · isometric deformations · rigidity
OP-00964 Open
Do reduced group C*-algebras remember torsion-free groups?
OA · C*-superrigidity · Peterson's operator algebra problems · reduced group C*-algebras · torsion-free groups
OP-00969 Open
Cocycle superrigidity of Bernoulli actions of groups with vanishing first ℓ²-Betti number
OA · Bernoulli actions · cocycle superrigidity · ℓ²-Betti numbers · Peterson's operator algebra problems
OP-00976 Open
Unitary representations of higher-rank lattices in the hyperfinite II₁ factor
OA · hyperfinite II₁ factor · lattices in Lie groups · Peterson's operator algebra problems · rigidity · unitary representations
OP-00979 Open
Unique Cartan subalgebras for groups with a nonzero ℓ²-Betti number
OA · Cartan subalgebras · C-rigidity · ℓ²-Betti numbers · Peterson's operator algebra problems