16.11.2017

Jonad Pulaj of the Mathematical Optimization Methods of ZIB group defended his thesis "Cutting Planes for Union Closed Families" at TU Berlin and thus successfully finished his studies in the Berlin Mathematical School. The thesis develops a novel method of computer-assisted theorem proving in extremal set theory, that aims at the solution of the famous Frankl conjecture. This conjecture states that any union-closed family of sets has an element in its ground set that is contained in at least half of the sets of the family. His method, which is based on exact integer programming, allowed Jonad Pulaj to prove the long standing 3-sets conjecture, which is related to the Frankl conjecture. He also disproved two conjectures of Morris and Vaughn, and gave hundreds of hitherto unknown so-called Frankl complete families of sets. The foto shows (from left to right) Martin Grötschel, Jonad Pulaj, Ralf Borndörfer, and John Sullivan, who acted as head of the PhD committee.