Structural Ramsey Theory
Speaker: Jan Reimann, Penn State
Abstract: Ramsey theory studies, in a most general sense, persistence of properties under partitions. Ramsey's theorem for the integers, for example, states that for every finite coloring of k-tuples of integers, there exists an infinite set of integers all whose k-tuples have the same color. Van der Waerden's theorem says that any finite partition of the integers has one set that contains arbitrarily long arithmetic progressions. Subsequent results showed that similar properties hold in certain objects were more structure is present, such as Boolean algebras or finite vector spaces. This gave rise to structural Ramsey theory, which can be seen as a categorical generalization of Ramsey theory on the integers. Structural Ramsey theory drew renewed interest this century following the so called KPT-correspondence between Ramsey properties and topological dynamics. In this talk, I will describe the basic results of structural Ramsey theory, with an eye towards developing the KPT-correspondence.
Room Reservation Information
Room Number: 315 McAllister
Time: 2:30pm - 4:00pm