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Nonlinear Phenomena in Evolutionary Partial Differential Equations
15:30 - 17:30, January 5, 2021 (Tuesday)
R440, Astronomy-Mathematics Building, NTU
(台灣大學天文數學館 440室)
Time-Frequency Analysis on Modulation Invariant Operators
Yung-Chang Hsu (National Taiwan University)


The Polynomial Carleson Operator correlates to the understanding of some parabolic PDE and serves as a basic model for operators with implicit higher-order modulation symmetry. Stein conjectured the full range bound of the operator, and Victor Lie proved exactly that in 2019 by rejuvenating Fefferman’s idea and introducing a framework for analysis on polynomial modulation. Later on, Pavel Zorin-Kranich generalized the result to a higher dimensional setting through the same philosophy and simplified some of the constructions in Lie’s arguments.
In this talk, aside from a brief history of the development, I will provide a heuristic explanation for Lie’s and Zorin-Kranich’s arguments, and, if time permits, we can discuss some interesting details.


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