6 problems

Let $R$ code a permutation group with no finite orbits, and let its age algebra over $\mathbb{C}$ be the associated graded algebra of finite relational structures up to isomorphism…

Let $G$ be a permutation group with no finite orbits, and let $\mathcal{A}^{G}$ be its Cameron algebra. Suppose in addition that $G$ is oligomorphic, meaning that it has finitely m…

Let $\mathcal{M}$ be an age-inexhaustible relational structure, meaning that any two finite substructures of $\mathcal{M}$ have disjoint copies within $\mathcal{M}$. Let the Camero…

Quasi-polynomiality conjecture. If $\varphi_R$ is bounded by some polynomial, then $\varphi_R$ is eventually a quasi-polynomial.

Let $R$ be a relational structure with profile $\varphi_R$. Assume that $R$ has bounded signature or finite kernel, and that $\varphi_R(n)$ is bounded by some polynomial in $n$. Ev…

Let $R$ be a relational structure with profile $\varphi_R$, and let the kernel of $R$ be finite. Assume that $\varphi_R(n)$ is bounded by some polynomial in $n$. Eventual quasi-pol…