Speaker: Joel Moreira (OSU)

Title: On $\{x + y, xy\}$ patterns in large sets of countable fields

Abstract:

In a previous joint work with V. Bergelson we showed that a large subset of a countable field K contains a non-trivial pair {x+y,xy} with x and y in K. Recently we obtained an alternative proof of this result. This new approach uses similar ergodic theoretical techniques together with limits along ultrafilters, and it gives some improvements on our previous work. In particular we show that a large subset of countable field with characteristic 0 contains a non-trivial pair {n+x,nx} where n is an integer and x is in K.