  The Frankl or Union-Closed Sets conjecture states that for any finite
union-closed family of sets $\mathcal{F}$ containing some nonempty set, there
is some element $i$ in the ground set $U(\mathcal F) := \bigcup_{S \in
\mathcal{F}} S$ of $\mathcal{F}$ such that $i$ is in at least half of the sets
in $\mathcal{F}$. In this work, we find new values and bounds for the least
integer $m$ such that any family containing $m$ distinct $k$-sets of an $n$-set
$X$ satisfies Frankl's conjecture with an element of $X$. Additionally, we
answer an older question of Vaughan regarding symmetry in union-closed families
and we give a proof of a recent question posed by Ellis, Ivan and Leader.
Finally, we introduce novel local configuration criteria to prove the
conjecture for many, previously unknown classes of families.
