6 problems

Classification conjecture. The invariant is a complete invariant of the set of equivalence classes modulo surgery in $\ker\rho$. Equivalently, the theorem asserting that there are…

Let $A\subset\mathbb{R}_{>0}$ be algebraically independent, meaning that no nonzero polynomial with rational coefficients vanishes on any finite tuple of distinct elements of $A$.…

Let a finite colouring of the plane be a colouring of $\mathbb{R}^2$ with finitely many colours, and say that it avoids a set of forbidden distances if no monochromatic pair of poi…

Let $X=\{0,1\}^{{\mathbf Z}_2*{\mathbf Z}_3}$ carry its canonical measure-preserving action of ${\mathbf Z}_2*{\mathbf Z}_3$. A colouring rule is stationarily essential when no sta…

Reconstruction–clustering threshold conjecture. The reconstruction threshold coincides with the clustering threshold.

Let $P$ be a finite set of points in the plane, and colour each point with one of $k$ colours. A monochromatic line means a maximal set of collinear points in $P$ whose points all…