Hall 123

Exponential patterns in arithmetic Ramsey theory

Sayan Goswami

IMSc

One of the primary goals in arithmetic Ramsey theory is to find out the family of subsets of N that are Ramsey, i.e., for any finite "coloring" (here coloring means partition) of N, there exists a member from that family that is the same color. One of the cornerstone theorems was due to I. Schur in 1918, when he proved that the family of sets {x,y,x+y} is Ramsey. Recently, J. Sahasrabudhe proved an exponential version of Schur's theorem. In this talk, we will discuss some recent developments in the direction of exponential patterns in Ramsey theory.