### Rutgers Discrete Mathematics Seminar

Title: Independent sets in hypergraphs

Speaker: **Jozsef Balogh**, University of Illinois

Date: Tuesday, October 16, 2012 2:00pm

Location: Hill Center, Room 525, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:
Many important theorems and conjectures in combinatorics, such as
the theorem of Szemer'edi on arithmetic progressions and the
Erd{H{o}}s-Stone Theorem in extremal graph theory, can be phrased as
statements about families of independent sets in certain uniform
hypergraphs. In recent years, an important trend in the area has been
to extend such classical results to the so-called `sparse random
setting'. This line of research has recently culminated in the
breakthroughs of Conlon and Gowers and of Schacht, who developed
general tools for solving problems of this type. Although these two
papers solved very similar sets of longstanding open problems, the
methods used are very different from one another and have different
strengths and weaknesses. In this talk, we explain a third, completely
different approach to proving extremal and structural results in
sparse random sets that also yields their natural `counting'
counterparts. We give a structural characterization of the independent
sets in a large class of uniform hypergraphs.

Joint work with Robert Morris and Wojciech Samotij.

See: http://math.rutgers.edu/seminars/allseminars.php?sem_name=Discrete%20Math