# Pure Maths Colloquium: Tuomas Orponen

This talk is part of the Pure Maths Colloquium at the University of St Andrews. Check out our upcoming talks at https://theran.lt/pure-colloquium/.

 Where: Zoom 812 4618 4775 When: Nov 4 2021 @ 16.00 Video: Link (internal)
 Speaker: Tuomas Orponen Jyväskylän yliopisto Title: Some products of recent work on sum-products

If $$A,B,C$$ are three finite sets in a field, under what assumptions can we find a point $$c$$ in $$C$$ such that $$A + cB$$ is much bigger than $$A$$? This is a variant of the Erdős-Szemerédi sum-product problem. I will briefly survey the problem in a number of fields. Then I will focus on the $$\delta$$-discretised version of the problem on the real line. This version is the most relevant one for fractal geometers.