Pacific Institute for the Mathematical Sciences - PIMS

Sticky Kakeya sets, and the sticky Kakeya conjecture

A Kakeya set is a compact subset of R^n that contains a unit line segment pointing in every direction. The Kakeya conjecture asserts that such sets must have dimension n. This conjecture is closely related to several open problems in harmonic analysis, and it sits at the base of a hierarchy of increasingly difficult questions about the behavior of the Fourier transform in Euclidean space.

There is a special class of Kakeya sets, called sticky Kakeya sets. Sticky Kakeya sets exhibit an approximate self-similarity at many scales, and sets of this type played an important role in Katz, Łaba, and Tao's groundbreaking 1999 work on the Kakeya problem. In this talk, I will discuss a special case of the Kakeya conjecture, which asserts that sticky Kakeya sets must have dimension n. I will discuss the proof of this conjecture in dimension 3. This is joint work with Hong Wang. 

Speaker Bio:Dr. Joshua Zahl is an associate professor at UBC and works in several fields of mathematical research: discrete mathematics, harmonic analysis, and geometric measure theory moving effortlessly between these fields. He has made useful and important contributions to the Kakeya problem as well as other problems in combinatorics and analysis. Zahl completed his Ph.D. in 2013 at UCLA; was an NSF postdoctoral fellow at MIT from 2013-2016; and joined the faculty at UBC in 2016. Outside of math, he explores the BC coast mountains.

See the announcement here.

Lecture location: ESB 2012

Lecture Time: 3:00pm Pacific 

Reception at PIMS: Room 4133 from 2:30 - 3:00pm

Join via Zoom:

https://ubc.zoom.us/j/68285564037?pwd=R2ZpLy9uc2pUYldHT3laK3orakg0dz09