Intersection Patterns: an unexpected application of the Erdos-Falconer distance problem

Time: 9:30 -- 11:00, June 7th, 2023.

Venue: Room 612, A6, Institute of Mathematics, VAST

Abstract: Let $A$ and $B$ be compact sets in $mathbb{R}^d$. One of the fundamental problems in Geometric Measure Theory is to study the relations between the Hausdorff dimensions of $A$, $B$, and $Acap f(B)$, where $f$ runs through a set of transformations. Many mathematicians have studied this type of question intensively, including Bishop, Elekes, Falconer, Mattila, Kahane, Keleti, Peres.... In this talk, I discuss recent results on the discrete analog of this topic. Our approach is based on a number of techniques including algebraic methods and discrete Fourier Analysis. This is joint work with Semin
Yoo (KIAS, Korea).