Jonathan Hickman- On Littlewood-Paley Theory for Space Curves

Explore Littlewood-Paley theory for space curves in this 45-minute lecture from the Hausdorff Center for Mathematics. Delve into the powerful tools of square function and Littlewood-Paley inequalities used in harmonic analysis, PDE, and analytic number theory to analyze functions with Fourier transforms supported in submanifold neighborhoods of R^n. Examine an approach to studying square functions associated with space curves, focusing on the careful analysis of sublevel sets of univariate polynomials. Discover how this robust method applies to various settings in number theory, including rings of congruence classes Z/NZ. Learn about the joint work of Jonathan Hickman and Jim Wright in this informative presentation on advanced mathematical concepts.