Return to Colloquia & Seminar listing
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 |
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