TTMS31. An introduction to Arithmetic Ramsey Theory
Speaker: Dr. Hoang Le, University of Mississippi
Abstract: Arithmetic Ramsey theory deals with structures that can be found in large subsets of the integers (e.g. sets of positive density, or sets coming from a finite partition of $\mathbf{Z}$). For example, Szemer\'edi's theorem, a cornerstone of this area, says that for any $k$, any set of positive density in $\mathbf{Z}$ must contain an arithmetic progression of length $k$. This area has intersection with number theory, combinatorics, Fourier analysis and dynamical systems. In this talk, I will give an accessible overview of the subject.