Lectures on Harmonic Analysis

IAS | PCMI Park City Mathematics Institute via YouTube

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YouTube
Pricing

Free Video
Languages

English
Duration & workload

22 hours 53 minutes
Sessions

On-Demand
Level

Advanced

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Explore advanced harmonic analysis through a comprehensive collection of lecture series from the 28th annual PCMI Summer Session held in Park City, Utah in 2018. Delve into six distinct 4-lecture courses delivered by leading mathematicians, covering cutting-edge topics in geometric measure theory, partial differential equations, and harmonic analysis. Study Camillo De Lellis's exposition of Almgren's Center Manifold theory in simplified settings, examining fundamental concepts in minimal surface theory and geometric variational problems. Learn quantitative unique continuation principles for second-order elliptic equations through Eugenia Malinnikova's detailed treatment of this crucial topic in partial differential equations. Investigate harmonic analysis techniques on non-smooth sets with Steve Hofmann's introduction to this challenging area, exploring how classical harmonic analysis extends to irregular geometric settings. Master the theory of homogenization for elliptic equations through Zhongwei Shen's systematic approach, covering convergence rates, uniform regularity estimates, and boundary value problems with oscillating data. Examine Aaron Naber's work on rectifiable Reifenberg theorems for measures, connecting geometric measure theory with harmonic analysis applications. Conclude with Guy David's treatment of sliding almost minimal sets and their connection to the Plateau problem, bridging classical variational problems with modern geometric analysis. Each lecture series provides deep mathematical insights suitable for graduate students and researchers working in harmonic analysis, partial differential equations, and geometric measure theory.

Syllabus

Camillo De Lellis, Almgren’s Center Manifold in a Simple Setting, part 1
Camillo De Lellis, Almgren’s Center Manifold in a Simple Setting, part 2.2
Camillo De Lellis, Almgren’s Center Manifold in a Simple Setting, part 2.1
Camillo De Lellis, Almgren’s Center Manifold in a Simple Setting, part 3.1
Camillo De Lellis, Almgren’s Center Manifold in a Simple Setting, part 3.2
Camillo De Lellis, Almgren’s Center Manifold in a Simple Setting, part 4.1
Camillo De Lellis, Almgren’s Center Manifold in a Simple Setting, part 4.2
Eugenia Malinnikova, Quantitative Unique Continuation for Solutions of Second Order Elliptic..., 1.1
Eugenia Malinnikova, Quantitative Unique Continuation for Solutions of Second Order Elliptic...,1.2
Eugenia Malinnikova, 1.3, Quantitative Unique Continuation for Solutions of Second Order Elliptic..
Eugenia Malinnikova, 2.1, Quantitative Unique Continuation for Solutions of Second Order Elliptic..
Eugenia Malinnikova, 2.2, Quantitative Unique Continuation for Solutions of ...
Steve Hofmann, An Introduction to Harmonic Analysis on Non-Smooth Sets, part 1.1
Steve Hofmann 2.1, An Introduction to Harmonic Analysis on Non-Smooth Sets
Eugenia Malinnikova, 3.1, Quantitative Unique Continuation for Solutions of Second Order...
Eugenia Malinnikova, 3 2, Quantitative Unique Continuation for Solutions of Second Order ..
Eugenia Malinnikova Quantitative Unique Continuation for Solutions of Second Order Elliptic.., 4.2
Steve Hofmann, 1.2, An Introduction to Harmonic Analysis on Non-Smooth Sets
Steve Hofmann 2.3, An Introduction to Harmonic Analysis on Non-Smooth Sets
Steve Hofmann 2.2, An Introduction to Harmonic Analysis on Non-Smooth Sets
Steve Hofmann, 3.1, An Introduction to Harmonic Analysis on Non-Smooth Sets
Steve Hofmann, 3.2, An Introduction to Harmonic Analysis on Non-Smooth Sets
Steve Hofmann, 4.1, An Introduction to Harmonic Analysis on Non-Smooth Sets
Steve Hofmann, 4.2, An Introduction to Harmonic Analysis on Non-Smooth Sets
Zhongwei Shen, Introduction to Homogenization of Elliptic Equations, lecture 1.1
Zhongwei Shen, Introduction to Homogenization of Elliptic Equations, lecture 1.2
Zhongwei Shen, Introduction to Homogenization of Elliptic Equations, 1.3
Zhongwei Shen, Convergence Rates, Lectures on Elliptic Homogenization 2.1
Zhongwei Shen, Convergence Rates, Lectures on Elliptic Homogenization 2.2
Zhongwei Shen, Uniform Regularity Estimates, lecture 3.1
Zhongwei Shen, Uniform Regularity Estimates, lecture 3.2
Zhongwei Shen, lecture 4.2, Boundary Value Problems with Oscillating Boundary Data,
Zhongwei Shen, lecture 4.1 Boundary Value Problems with Oscillating Boundary Data
Aaron Naber, Rectifiable Reifenberg for Measures, 1.1
Aaron Naber, Rectifiable Reifenberg for Measures, 1.2
Aaron Naber, Rectifiable Reifenberg for Measures, 2.1
Aaron Naber, Rectifiable Reifenberg for Measures, 2.2
Guy David, Sliding Almost Minimal Sets and the Plateau Problem, 1.1
Guy David, Sliding Almost Minimal Sets and the Plateau Problem, 1.2
Guy David, Sliding Almost Minimal Sets and the Plateau Problem, 2.1
Guy David, Sliding Almost Minimal Sets and the Plateau Problem, 2.2
Aaron Naber, Rectifiable Reifenberg for Measures, 3.1
Aaron Naber, Rectifiable Reifenberg for Measures, 3.2
Guy David, Sliding Almost Minimal Sets and the Plateau Problem, 3.2
Guy David, Sliding Almost Minimal Sets and the Plateau Problem, 3.2
Aaron Naber, Rectifiable Reifenberg for Measures, 4.2
Aaron Naber, Rectifiable Reifenberg for Measures, 4.1
Guy David, Sliding Almost Minimal Sets and the Plateau Problem, 4.2
Guy David, Sliding Almost Minimal Sets and the Plateau Problem, 4.1