Harmonic Analysis - PCMI 28th Annual Summer Session 2018

IAS | PCMI Park City Mathematics Institute via YouTube

Start learning Write review

Details

Start learning

Provider

YouTube
Pricing

Free Video
Languages

English
Duration & workload

22 hours 53 minutes
Sessions

On-Demand
Level

Advanced

Found in

Explore advanced harmonic analysis through this comprehensive lecture series from the 28th Annual PCMI Summer Session featuring leading mathematicians presenting cutting-edge research and foundational concepts. Delve into Camillo De Lellis's detailed exposition of Almgren's Center Manifold theory presented in a simplified setting, covering fundamental principles and applications across multiple sessions. Master quantitative unique continuation for solutions of second-order elliptic equations through Eugenia Malinnikova's systematic treatment of this important topic in partial differential equations. Investigate harmonic analysis on non-smooth sets with Steve Hofmann's introduction to this specialized area, examining how classical harmonic analysis techniques extend to irregular geometric settings. Study the homogenization of elliptic equations with Zhongwei Shen's lectures covering convergence rates, uniform regularity estimates, and boundary value problems with oscillating boundary data. Examine Aaron Naber's work on rectifiable Reifenberg theory for measures, exploring connections between geometric measure theory and harmonic analysis. Conclude with Guy David's presentation on sliding almost minimal sets and their relationship to the Plateau problem, bridging variational calculus and geometric analysis. Each topic is presented through multiple detailed sessions allowing for deep exploration of theoretical foundations, proof techniques, and current research directions in modern harmonic analysis.

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