Title: Euclidean Ramsey theory over finite fields
Speaker: Hans Parshall (The Ohio State University)
Abstract: Euclidean Ramsey theory attempts to classify the so-called Ramsey sets: those finite point configurations which must be preserved up to congruence in partitions of Euclidean space. While we have many examples of Ramsey sets, a reasonable classification remains the subject of two wildly inconsistent conjectures. We will discuss some recent progress on a finite field model, joint with Neil Lyall and Ákos Magyar, in which we use a Gowers-style uniformity approach to go beyond what is known in the Euclidean setting.
Note: The goal of Welcome Seminar is to give an opportunity to new postdoctoral fellows and tenure track professors to introduce themselves to their colleagues. The talks are intended to be non-technical and accessible to graduate students as well. Please plan to attend and encourage your graduate students to do so as well. The talk will be preceded by a colloquium-style reception at 4:00, in the area adjacent to Cockins Hall 240 on the second floor of the Math Building.