2 problems

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Lev's periodicity conjecture for large maximal sum-free sets in $\mathbb F_3^n$
Lev's periodicity conjecture. If
Conjecturesolvedadditive-combinatorics finite-vector-spaces sum-free-setsarXiv posted 2 days ago
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The balls conjecture for maximal cross-intersecting families of vectors
The balls conjecture. There exists a maximal pair of $r$ -cross-intersecting families $A,B\subseteq S_p$ in which both $A$ and $B$ are balls. If $p_i\ge3$ for all $i\in[n]$ , then ev…
Conjectureopenextremal-combinatorics finite-vector-spaces intersecting-familiesarXiv posted 2 days ago

Lev's periodicity conjecture for large maximal sum-free sets in F3n\mathbb F_3^nF3n​