Director’s Cuts is delighted to have Prof. Larry Guth (MIT) speak on “An enemy scenario in restriction theory”.
The (live) talk will be given on Wednesday, March 2 at 3pm EST. This is a joint event hosted together with the AIM Research Community “Fourier restriction conjecture and related problems“. Please see below for the Zoom link and the abstract of the talk.
Soon after the live event, the recording of the talk will be posted on our channel. Prof. Guth has also kindly agreed to host an office hour on our platform taking questions and discussing more about the content of the talk with interested viewers. The office hour will be held on Wednesday, March 16, from 3pm-4pm EDT.
Join the live talk on March 2, 3pm EST:
Join the office hour on March 16, 3pm EDT:
Anyone is welcome!
Abstract: The goal of this talk is to explore some of the difficulties
involved in an open problem in restriction theory. The problem is the
Mizohata-Takeuchi conjecture for the parabola, which is a special case of
a conjecture Stein raised. This is a conjecture about weighted estimates
for the extension operator for the parabola. While we focus on this
problem for concreteness, I think that there are similar difficulties
involved in a number of open problems in restriction theory.
A lot of work in restriction theory leans heavily on wave packet
decompositions, and on a short list of basic properties of wave packet
decompositions. For instance, the proof of decoupling for the parabola
(or paraboloid or moment curve) only uses this list of basic properties.
We will describe an enemy scenario for the M-T conjecture. This scenario
would respect the basic properties of wave packet decompositions used in
decoupling, but would violate the M-T conjecture. I don’t know whether
this scenario actually happens. In order to rule out this scenario,
we would have to find a new tool.