### DIMACS - Graduate Student Combinatorics Seminar

Title: The Union-Closed Sets Conjecture

Speaker: **Abigail Raz**, Rutgers University

Date: Wednesday, February 15, 2017 12:10pm

Location: Graduate Student Lounge, 7th Floor, Hill Center, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

The union-closed sets conjecture states that for any union closed family of sets with only finitely many member sets (and not only the empty set) there is an element appearing in at least half the sets. In this talk we will discuss a few weaker results that hold for union closed families motivated by the conjecture. Additionally, time permitting we will discuss a few reformulations of the conjecture in the language of lattices and graphs. We will state, and maybe even prove, that the conjecture is true for certain families.

See: http://www.math.rutgers.edu/~ajr224/GCS.html