= Will Sawin
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<Will Sawin> works on problems connecting arithmetic and <combinatorics>. His paper on the <union-closed sets conjecture> applies <entropy> inequalities to a finite family closed under unions.<An improved lower bound for the union-closed sets conjecture by Will Sawin>[Original byline and abstract]{ref}
For a nontrivial such family, the paper guarantees an element in at least a $(3-\sqrt5)/2$ fraction of the sets. The argument studies the union of independent random members and bounds the resulting entropy growth. It is a quantitative advance toward the conjectured one-half fraction, with the nonempty-union condition needed to exclude the family containing only the empty set.<An improved lower bound for the union-closed sets conjecture by Will Sawin>[Theorems 1–2 and family application]{ref}
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