Sharp Fourier Restriction onto the Parabola and the Cubic Monomial - Lecture 1

Explore the intricacies of Sharp Fourier restriction onto the parabola and the cubic monomial in this lecture by Chandan Biswas, part of the "Modern Trends in Harmonic Analysis" program at the International Centre for Theoretical Sciences. Delve into cutting-edge developments in harmonic analysis, focusing on polynomial methods and their applications to Fourier restriction and Bochner-Riesz conjectures. Gain insights into the powerful techniques of algebraic geometry used to solve outstanding problems in the field. Learn about the recent advancements in discrete harmonic analysis and their connections to number theory. Discover how sparse domination techniques are applied to address challenges related to discrete averages and maximal functions. Benefit from this comprehensive overview of new methodologies in harmonic analysis, preparing you for potential research projects in these exciting areas.