2 problems

Matching

The multiplicity-two conjecture for the second Dirichlet eigenvalue on simply connected planar domains
About 4 years old
Multiplicity-two conjecture.
openeigenvalue-multiplicities planar-domains spectral-geometry
011
The conjectured formula for the first minimum zero eigenvalue multiplicity
At least 7 years old
Conjectured identity. For $w\geq 5$ and $n\geq 2w+1$ ,
openeigenvalue-multiplicities extremal-combinatorics johnson-scheme
09