Mathematical Sciences Department Seminar
Bob Krueger, Carnegie Mellon
Friday, January 31
2:00 - 3:00 pm
Stratton 207
An introduction to Ramsey Theory
In any group of six people, there are either at least three people who all know each other, or at least three people who all do not. Ramsey Theory is a branch of combinatorics and logic that studies many generalizations of this fact, with the common theme being "in any sufficiently large system, some structures are unavoidable." I will give an introduction to this area, showcasing the utility of algorithmic and probabilistic approaches to these problems. I will also mention two recent, exciting breakthroughs on some of the hardest problems in Ramsey Theory.