clopen.solutions

Open problems

1131 registered problems.

OP-01051 Solution claimed
Do L(F₂) and L(F₃) have isomorphic ultrapowers?
OA · elementary equivalence · free group factors · Peterson's operator algebra problems · ultrapowers
OP-01052 Solution claimed
Invariance of free entropy dimension under change of generators
OA · free entropy dimension · free probability · II₁ factors · Peterson's operator algebra problems
OP-01053 Solution claimed
Are ℓ²-Betti numbers of groups invariants of their group von Neumann algebras?
OA · group von Neumann algebras · ℓ²-Betti numbers · Peterson's operator algebra problems · W*-invariants
OP-01054 Solution claimed
Connes's rigidity conjecture for property (T) groups
OA · Connes's rigidity conjecture · group von Neumann algebras · Peterson's operator algebra problems · property (T) · W*-rigidity
OP-01055 Solution claimed
Connes's rigidity conjecture for lattices in higher-rank simple Lie groups
OA · Connes's rigidity conjecture · lattices in Lie groups · Peterson's operator algebra problems · W*-rigidity
OP-01056 Solution claimed
Popa's strong form of Connes's rigidity conjecture for higher-rank lattices
OA · amplifications · Connes's rigidity conjecture · lattices in Lie groups · Peterson's operator algebra problems · W*-superrigidity
OP-01057 Solution claimed
Fundamental group of the group factor of PSLₙ(ℤ)
OA · fundamental group of II₁ factors · lattices in Lie groups · Peterson's operator algebra problems · property (T)
OP-01058 Solution claimed
Do the group factors of PSLₙ(ℤ) remember n?
OA · group von Neumann algebras · lattices in Lie groups · Peterson's operator algebra problems · W*-rigidity
OP-01059 Needs verification
Finitely many groups with the same group factor, for property (T) groups
OA · group von Neumann algebras · Peterson's operator algebra problems · property (T) · W*-rigidity
OP-01060 Solution claimed
The Kadison–Ringrose vanishing cohomology conjecture
OA · derivations · Hochschild cohomology · Peterson's operator algebra problems · von Neumann algebras
OP-01061 Solution claimed
The invariant subspace problem relative to a von Neumann algebra
OA · invariant projections · invariant subspace problem · Peterson's operator algebra problems · von Neumann algebras
OP-01062 Solution claimed
Kadison's problem on orthonormal bases of unitaries in II₁ factors
OA · II₁ factors · orthonormal bases · Peterson's operator algebra problems · unitaries
OP-01063 Solution claimed
Is the reduced C*-algebra of the free group on countably infinitely many generators finitely generated?
OA · free groups · generator problem · Peterson's operator algebra problems · reduced group C*-algebras
OP-01064 Solution claimed
Is there a group that is not sofic?
GR · group approximation · Peterson's operator algebra problems · sofic groups
OP-01065 Solution claimed
Is Thompson's group F amenable?
GR · amenability · Peterson's operator algebra problems · Thompson's group F
OP-01066 Solution claimed
The rigidity problem for uniform Roe algebras of uniformly locally finite coarse spaces
OA · coarse geometry · Peterson's operator algebra problems · rigidity · uniform Roe algebras
OP-01067 Solution claimed
Is every quasitrace on a C*-algebra a trace?
OA · AW*-algebras · C*-algebras · Peterson's operator algebra problems · quasitraces
OP-01068 Open
Voronoi diagram of lines in three dimensions
MG · lower envelopes · The Open Problems Project · Voronoi diagram of lines
OP-01069 Open
Union of fat objects in three dimensions
MG · fat objects · The Open Problems Project · union complexity
OP-01070 Open
Maximum number of k-sets
CO · halving lines · k-sets · The Open Problems Project
OP-01071 Open
Strongly polynomial linear programming
OC · linear programming · strongly polynomial algorithm · The Open Problems Project
OP-01072 Open
Point location in three-dimensional subdivisions
MG · point location · spatial subdivisions · The Open Problems Project
OP-01073 Open
Counting simple polygonalizations of a point set
CO · counting non-crossing Hamiltonian cycles · simple polygonalization · The Open Problems Project
OP-01074 Open
Recognizing visibility graphs of simple polygons
CO · simple polygon · The Open Problems Project · visibility graph recognition
OP-01075 Open
Complexity of vertical decompositions in five and more dimensions
MG · arrangements of surfaces · The Open Problems Project · vertical decomposition
OP-01076 Open
Subquadratic minimum-link paths among planar obstacles
MG · link distance · minimum-link path · The Open Problems Project
OP-01077 Open
Illuminating polygons with vertex π-floodlights
MG · art gallery problem · floodlight illumination · The Open Problems Project
OP-01078 Open
Hexahedral meshes compatible with a quadrilateral surface mesh
MG · hexahedral mesh · quadrilateral mesh · The Open Problems Project
OP-01079 Open
Flip-graph connectivity of tetrahedralizations in three dimensions
MG · flip graph · tetrahedralization · The Open Problems Project
OP-01080 Open
Hamiltonian tetrahedralizations of convex polytopes
MG · dual graph · Hamiltonian path · tetrahedralization · The Open Problems Project
OP-01081 Open
Maximum number of edges in a thrackle
CO · Conway's thrackle conjecture · graph drawing · The Open Problems Project · thrackle
OP-01082 Open
Trapping the light of a point source with segment mirrors
MG · light trapping · mirrors · polygonal billiards · The Open Problems Project
OP-01083 Open
Extending pseudosegment arrangements to pseudoline arrangements by subdivision
MG · pseudoline arrangements · pseudosegments · The Open Problems Project
OP-01084 Open
Complexity and approximation of the freeze-tag problem
OC · approximation algorithms · freeze-tag problem · NP-hardness · The Open Problems Project
OP-01085 Open
Compatible triangulations of point sets
MG · compatible triangulations · morphing · point sets · The Open Problems Project
OP-01086 Open
Pointed pseudotriangulations versus triangulations
CO · counting triangulations · pseudotriangulations · The Open Problems Project
OP-01087 Open
Sorting X+Y
CO · pairwise sums · sorting X+Y · The Open Problems Project
OP-01088 Open
Vertex-unfolding polyhedra
MG · polyhedra · The Open Problems Project · vertex-unfolding
OP-01089 Open
General unfoldings of nonconvex polyhedra
MG · general unfolding · nonconvex polyhedra · The Open Problems Project
OP-01090 Open
3-colorability of great-circle arrangements
CO · arrangements of great circles · graph coloring · The Open Problems Project · zonohedra
OP-01091 Open
Smallest universal point sets for planar graphs
CO · straight-line drawings of planar graphs · The Open Problems Project · universal point sets
OP-01092 Open
Two-bend 3D orthogonal point-drawings of graphs of maximum degree six
CO · 3D orthogonal graph drawing · bends · The Open Problems Project
OP-01093 Open
Planar Euclidean maximum traveling salesman problem
MG · Euclidean distances · maximum traveling salesman problem · The Open Problems Project
OP-01094 Open
Traveling salesman problem in solid grid graphs
CO · Hamiltonian cycle · solid grid graphs · The Open Problems Project · traveling salesman problem
OP-01095 Open
Complexity of the pallet loading problem
OC · computational complexity · pallet loading · rectangle packing · The Open Problems Project
OP-01096 Open
Chromatic number of the plane
CO · chromatic number of the plane · Hadwiger–Nelson problem · The Open Problems Project · unit-distance graph
OP-01097 Open
Three-colorings of the plane with no monochromatic congruent triangle
CO · Euclidean Ramsey theory · monochromatic triangle · plane coloring · The Open Problems Project
OP-01098 Solution claimed
Transforming polygons into regular polygons by vertex-centroid moves
MG · polygon transformation · regular polygon · The Open Problems Project · vertex centroid
OP-01099 Open
Number of lines tangent to four unit balls
MG · combinatorial complexity · lines tangent to balls · line transversals · The Open Problems Project
OP-01100 Open
Volume-maximizing convex shape under perimeter-halving folding
MG · Alexandrov gluing · folding convex polygons · perimeter halving · The Open Problems Project