Combinatorics: Orit Raz (HUJI)

Mon, 11/10/202115:00-17:00
B400 CS building
HUJI Combinatorics Seminar 

When: Monday October 11th, 2021, at 3PM (Israel time)

Where: B400 in CS\Engineering building

Speaker:  Orit Raz (HUJI)

The pinned Falconer’s distance problem and related problems


For a Borel set A\subset R^2 and a point p\in R^2, consider the pinned distance set
D_p(A) = { |p-q|  |  q\in A }.
In a recent result, joint with Josh Zahl, we study the set of exceptional points, for which the pinned distance has small Hausdorff dimension, that is, close to (dim A)/2. We show that if this set has positive dimension, then it must have very special structure. 

In the talk I will explain how this result follows from a single scale estimate, which is an analogue of the problem in the setting of the Katz-Tao discretized ring conjecture. I will then tell about some steps in the proof of the discretized statement, and compare them to the proof of an analogue statement in the discrete setting.