2 problems

Conjecture on simple wavelet sets for expansive matrices. If $|\det A|\ne 2$, then $A$ can have a simple wavelet set if and only if $A$ has a positive integer power equal to a scal…

Soardi–Wieland–Benedetto–Sumetkijakan conjecture. A wavelet set for dilation by $2$ in dimension greater than $1$ cannot be written as a finite union of convex sets.