Projections and circles

Speaker: Malabika Pramanik

Date: Thu, Apr 7, 2022

Location: PIMS, University of Victoria, Online

Conference: PIMS-UVic Department Colloquium

Subject: Mathematics

Class: Scientific


Large sets in Euclidean space should have large projections in most directions. Projection theorems in geometric measure theory make this intuition precise, by quantifying the words “large” and “most”.

How large can a planar set be if it contains a circle of every radius? This is the quintessential example of a curvilinear Kakeya problem, central to many areas of harmonic analysis and incidence geometry.

What do projections have to do with circles?

The talk will survey a few landmark results in these areas and point to a newly discovered connection between the two.