Upcoming Talks in Probability and Dynamics Seminar, UVic
Speaker: Saúl Rodríguez Martín (Ohio State University)
Time: 13 November, 2026, 11:30 a.m. - 12:30 p.m.
Location: Zoom
Title: An ergodic approach to equations of the form $x+y=\lfloor \alpha(n)\rfloor$.
Abstract: Khalfalah and Szemerédi proved in 2006 that every finite coloring of the positive integers contains distinct monochromatic integers $x$ and $y$ such that $x+y=n^2$, for some natural $n$. In this talk, we will discuss an ergodic approach to equations of the form $x+y=\lfloor \alpha(n)\rfloor$, where $\alpha(x)$ is a Hardy field function of polynomial growth, such as $x^7\log(x), x^3+\log(x)^2$ or $x^\pi$. We will see when such equations have solutions with $x,y$ lying either in the same cell of a given finite partition of the positive integers or in a given set of positive upper density. This is joint work with Vitaly Bergelson and Hao Pan.
Speaker: Manan Bhatia (University of Geneva)
Time: 20 November, 2026, 11:30 a.m. - 12:30 p.m.
Location: TBD
Title: TBD
Abstract: TBD