### Ilan Karpas

Tuesday, December 18, 2018, 10:45 – 11:45, -101

Abstract:

A union closed family F is a family of sets, so that for any two sets A,B in F, A$\cup$B is also on F. Frankl conjectured in 1979 that for any union-closed family F of subsets of [n], there is some element i $\in$ [n] that appears in at least half the members of F.

 We prove that the conjecture is true if F >= 2^{n-1}, using tools from boolean analysis.