Month: November 2014

Seminar 11.20.14 Moreira

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.

Seminar 11.13.2014 Robertson

Speaker: Donald Robertson (Ohio State)

Title: The Corners Theorem for Quasirandom Groups

Abstract: The corners theorem, proved by Ajtai and Szemeredi in 1974, states that for any prescribed density, any dense subset of a large enough n-by-n grid contains the vertices of a right triangle. In this talk I will describe recent joint work with V. Bergelson and P. Zorin-Kranich on a version of the corners theorem for quasirandom groups (finite groups without low-dimensional complex representations) via ergodic theory.