UVictoria Discrete Math Seminar: Yuveshen Mooroogen

In recent years, harmonic analysts and fractal geometers have become increasingly interested in Ramsey-theoretic problems for subsets of Rn. Many of these were inspired by discrete analogues.

Over the past 20 years, classical theorems from discrete mathematics—including Roth’s 3-term arithmetic progression theorem, the Furstenberg–Sárközy theorem on perfect square differences, and the Salem–Spencer arithmetic-progression-free sets—have been successfully translated to the real-number setting.

In the first half of this talk, I will highlight some of these Euclidean analogues and explain how they arose. In the second, I will discuss my recent work on a variant of an old problem of Erdős concerning the (non-)existence of sequences inside “large” sets.

The talk assumes minimal background. You may find familiarity with Lebesgue measure useful, but it’s enough to think of it as length. No fractal geometry experience is required.