2 papers
math.CA2026
Furstenberg-type estimates under mild non-concentration assumptions
Tuomas Orponen, Pablo Shmerkin
We prove sharp -discretised versions of some variants of the Furstenberg set problem under weaker or different non-concentration assumptions compared to previous works.
math.CA2025
Simple proofs of discretised projection theorems
William O'Regan, Pablo Shmerkin, Hong Wang
We give a simple, short and self-contained presentation of Bourgain's discretised projection theorem from 2010, which is a fundamental tool in many recent breakthroughs in geometri…