The dimension spectrum conjecture for lines

Abstract: Effective dimension gives a fine-grained measure of randomness of individual points in Euclidean space. Let L be a line in the Euclidean plane. The dimension spectrum sp(L) is the set of all effective dimensions of individual points on L. Jack Lutz, in the early 2000s, posed the dimension spectrum conjecture. This conjecture states that, for every line L, sp(L) contains a unit interval. In this talk, we present a proof of the dimension spectrum conjecture. We also discuss its relation to open problems in geometric measure theory, and avenues for future research.

logic

Audience: researchers in the topic

Computability theory and applications

Series comments: Description: Computability theory, logic

The goal of this endeavor is to run a seminar on the platform Zoom on a weekly basis, perhaps with alternating time slots each of which covers at least three out of four of Europe, North America, Asia, and New Zealand/Australia. While the meetings are always scheduled for Tuesdays, the timezone varies, so please refer to the calendar on the website for details about individual seminars.