3 problems

Let $q$ be an odd prime power satisfying $q\equiv1\pmod4$ and $q^2\equiv1\pmod5$, and let $\sigma(\operatorname{PSL}_2(q))$ denote the intersection spectrum. Meagher's intersection…

Erdős–Lovász conjecture. The size of the intersection spectrum tends to infinity with $k$:

Let $q$ range over odd prime powers with $q\equiv1\pmod4$. For a subgroup of $\operatorname{PSL}_2(q)$ isomorphic to $\mathbb{Z}_{\frac{q-1}{2}}$, consider the action of…