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Uniform boundedness in operators parametrized by polynomial curves
Student-Run Analysis & PDE| Speaker: | Jauma de Dios Pont, University of California, Los Angeles |
| Related Webpage: | https://jaume.dedios.cat/ |
| Location: | Zoom |
| Start time: | Thu, Feb 11 2021, 1:10PM |
Description
Multiple
results in harmonic analysis involving integrals of functions over
curves (such as restriction theorems, convolution estimates, maximal
function estimates or decoupling estimates) depend strongly on the
non-vanishing of the torsion of the associated curve. Over the past
years there has been considerable interest in extending these results to
a degenerate case where the torsion vanishes at a finite number of
points by using the affine arc-length as an alternative integration
measure. As a model case, multiple results have been proven in which the
coordinate functions of the curve are polynomials. In this case one
expects to find bounds on the operators that depend only on the degree
of the polynomial.
In this talk I will introduce and motivate the concept of affine
arclength measure, provide a new decomposition theorem for polynomial
curves over characteristic zero local fields, and show some applications
to uniformity results in harmonic analysis.
Zoom link: https://ucdavis.zoom.us/j/91748527825?
Passcode: first six digits of pi