An Incidence Result for Well-Spaced Atoms.
9th February 2021, 11:00 am – 12:00 pm
Virtual (online) Zoom seminar; a link will be sent to the Bristol Combinatorics Seminar mailing list, the week before the seminar.
In this talk we will give details of an incidence result for well-spaced \delta-balls (or \delta-atoms) in [0,1]^d. The result numerically matches the bound predicted by the Szemeredi-Trotter Theorem. The methods are inspired by a 2019 paper of Guth, Solomon and Wang, and use a combination of techniques from combinatorics and Fourier analysis. We also prove a continuous analogue of Beck's Theorem in all dimensions d \geq 2 as an application.