clopen.solutions

Open problems

980 registered problems.

OP-00812 Solution claimed
Minimal persistence grids versus homological Morse lower bounds
AT · AIM Open Applied Problems · multigraded Betti numbers · multiparameter persistent homology
OP-00824 Solution claimed
Limiting Betti-number distributions in preferential-attachment networks
PR · AIM Open Applied Problems · Betti numbers · clique complexes · preferential attachment
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-00970 Open
Trivial fundamental group for Bernoulli crossed products
OA · Bernoulli actions · fundamental group of II₁ factors · ℓ²-Betti numbers · Peterson's operator algebra problems
OP-00973 Open
Cost of a group and its first ℓ²-Betti number
GR · cost · ℓ²-Betti numbers · measured group theory · Peterson's operator algebra problems
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