6 problems

Dimension conjecture. For all $0 < \lambda < \mu < 1$ with $\lambda + \mu > 1$, the set $A_{\lambda,\mu}$ has dimension strictly greater than $1$.

Top-boundary conjecture. For all $0 < \lambda < \mu < 1$ with $\lambda + \mu > 1$, the set $\partial_{top}(A_{\lambda,\mu})$ is the graph of a continuous, strictly increasing funct…

Bi-Lipschitz rigidity conjecture. If 2-attractors are not affinely similar, then they are not bi-Lipschitz equivalent.

A uniformly random self-affine set is obtained as the attractor of a random iterated function system of affine contractions, with the randomness specified by the model under consid…

Let $A\in M_2(\mathbb{Z})$ be expanding with $|\det(A)|=3$, let $f$ be its characteristic polynomial, and let ${\mathcal{D}}=\{0,1,b\}v$ with $b>1$ and $v\in\mathbb{R}^2$ such that…

Isometric-copy translation conjecture. There exists a translation $t$ such that