## Olivetti Club

Itamar OliveiraCornell University
From needles and tubes to Fourier multipliers and beyond
Tuesday, September 5, 2017 - 4:30pm
Malott 406

In this talk we will introduce many versions of what is known as the Kakeya problem. One such version is the following: what is the smallest possible measure of a set in $\mathbb{R}^{n}$ that contains a unit line segment (needle) parallel to every direction? What if we want to continuously rotate the needle inside this set, does the answer change? This kind of problem was investigated independently by Besicovitch and Kekeya when the first was studying some properties of the Riemann integral. We will also present some conjectures involving these sets that are (surprisingly) related to the famous Restriction conjecture in Harmonic Analysis and comment of the celebrated work of C. Fefferman about the multiplier problem for the ball.

Refreshments will be served in the lounge at 4:00 PM.