6 problems

Let $k$ be a Hilbertian field. A finite split embedding problem over $k$ is an epimorphism … where $G$ is finite, $L/k$ is Galois, and there is an embedding…

Generalized Menger embedding conjecture. The van Kampen obstruction of $K\times L$ is non-zero.

A hypertree is a connected, simple $3$-uniform hypergraph in which every two vertices are joined by a unique path. A Steiner triple system is a $3$-uniform hypergraph in which ever…

Let $(X,\mathbb{Z}^k)$ be a dynamical system, and for each subgroup $A$ of $\mathbb{Z}^k$ define … The quotient group $\mathbb{Z}^k/A$ acts naturally on $X_A$; when the quotient is…

Codimension-1 Grassmannian embedding conjecture. The only codimension-$1$ smooth embedding

Let $k$ and $m$ be positive integers. A simple partial $k$-latin square is a partial $k$-latin square in which no symbol is repeated within a cell. Eventual embedding conjecture. T…