Harmonic Analysis Courses and Certifications

Institute for Advanced Study

Analysis and Mathematical Physics

Explore advanced mathematical physics through expert lectures on quantum systems, fluid dynamics, spectral theory, geometric analysis, and cutting-edge research from leading mathematicians and physicists.

• YouTube
• 3 days 8 hours 42 minutes
• On-Demand
• Free Video

Projection Theory - Spring 2025

Explore advanced projection theory connecting geometry, harmonic analysis, and combinatorics through studying objects via their shadows in different directions.

• YouTube
• 1 day 7 hours 32 minutes
• On-Demand
• Free Video

Centre International de Rencontres Mathématiques

Computational Time-Frequency and Coorbit Theory

Explore advanced mathematical analysis through computational time-frequency methods, coorbit theory, and function spaces with applications to wavelets, Gabor frames, and operator theory.

• YouTube
• 12 hours 20 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Union of Tubes and Kakeya Sets - 3/3

Explore advanced techniques like Cordoba argument and projection theory to prove volume bounds on tube unions in R² and R³, with applications to the challenging Kakeya problem.

• YouTube
• 2 hours 40 minutes
• On-Demand
• Free Video

The Bourgain Projection Theorem Part 3 - Lecture 16

Explore robust estimates in multiscale arguments within the Bourgain Projection Theorem framework through advanced mathematical analysis and theoretical foundations.

• YouTube
• 1 hour 20 minutes
• On-Demand
• Free Video

Sharp Projection Theorems Part 3 - Combining Different Scales - Lecture 24

Explore how Ren and Wang proved the full Furstenberg conjecture by applying the AD regular case across multiple scales in advanced projection theory.

• YouTube
• 1 hour 17 minutes
• On-Demand
• Free Video

The Bourgain-Katz-Tao Projection Theorem - Lecture 12

Explore the groundbreaking Bourgain-Katz-Tao projection theorem from the early 2000s, which revolutionized projection theory by introducing techniques beyond traditional methods.

• YouTube
• 1 hour 18 minutes
• On-Demand
• Free Video

ICTP Mathematics

Basic Notions Seminar on Fourier Optimization and Number Theory

Explore the intersection of harmonic analysis and analytic number theory, including problems related to the Riemann hypothesis, in this advanced mathematics seminar.

• YouTube
• 1 hour 13 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Jonathan Hickman- On Littlewood-Paley Theory for Space Curves

Explore Littlewood-Paley inequalities for functions with Fourier transforms near submanifolds, focusing on space curves and applications in harmonic analysis, PDE, and number theory.

• YouTube
• 45 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Sharp Examples for Decoupling and Related Questions

Explore open questions in decoupling, examining sharp examples and their connections to number theory and harmonic analysis. Gain insights into current challenges in the field.

• YouTube
• 49 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Some Sharp Strichartz Inequalities

Explore sharp Strichartz inequalities for Schrödinger equations, focusing on planar power curves and extremizers. Gain insights into concentration-compactness and fourth-order equations in one dimension.

• YouTube
• 44 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Estimates for Bochner-Riesz Means at the Critical Index by David Beltran

Explore advanced harmonic analysis techniques, focusing on Bochner-Riesz means estimates at the critical index. Gain insights into cutting-edge research and applications in this specialized mathematical field.

• YouTube
• 1 hour 52 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Endpoint Eigenfunction Bounds for the Hermite Operator by Sanghyuk Lee

Explore endpoint eigenfunction bounds for the Hermite operator, delving into advanced harmonic analysis concepts and recent developments in mathematical research.

• YouTube
• 1 hour 55 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Nikodym Sets and Maximal Functions Associated with Spheres - Lecture 1

Explore advanced harmonic analysis concepts: Nikodym sets and maximal functions associated with spheres. Gain insights from expert Jongchon Kim in this comprehensive lecture.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Global Maximizers for Spherical Restriction by Diogo Oliveira e Silva

Explore global maximizers for spherical restriction in harmonic analysis. Gain insights into recent developments and techniques in this cutting-edge mathematical field.

• YouTube
• 1 hour 9 minutes
• On-Demand
• Free Video