3 problems

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Guralnick–Tiep derangement conjecture for primitive affine groups
Let $G$ be a primitive affine permutation group of degree $n$ , and suppose that $G$ is non-Frobenius. Write $\delta(G)$ for the proportion of elements of $G$ that are derangements.…
Conjectureopenaffine-groups derangements permutation-groupsarXiv posted 2 days ago
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Mann–Praeger–Seress conjecture on extremely primitive affine groups
Mann–Praeger–Seress conjecture. None of the affine candidates omitted from that list are extremely primitive.
Conjectureopenaffine-groups finite-groups permutation-groupsarXiv posted 2 days ago
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The energy bound conjecture for finite subsets of the affine group
Let $A$ be a finite set of transformations in the affine group $\operatorname{Aff}(\mathbb{F})$ , and suppose that no line contains more than $M$ points of $A$ . Write $E(A)$ for the…
Conjectureopenadditive-combinatorics affine-groups energy-estimatesarXiv posted 2 days ago

Guralnick–Tiep derangement conjecture for primitive affine groups