**IAS/Park City Mathematics Series**

Volume: 27;
2020;
345 pp;
Hardcover

MSC: Primary 42; 53; 35; 28;

**Print ISBN: 978-1-4704-6127-0
Product Code: PCMS/27**

List Price: $110.00

AMS Member Price: $88.00

MAA Member Price: $99.00

**Electronic ISBN: 978-1-4704-6281-9
Product Code: PCMS/27.E**

List Price: $110.00

AMS Member Price: $88.00

MAA Member Price: $99.00

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# Harmonic Analysis and Applications

Share this page *Edited by *
*Carlos E. Kenig; Fang Hua Lin; Svitlana Mayboroda; Tatiana Toro*

A co-publication of the AMS, IAS/Park City Mathematics Institute, and Society for Industrial and Applied Mathematics

The origins of the harmonic analysis go back to an ingenious idea of
Fourier that any reasonable function can be represented as an infinite
linear combination of sines and cosines. Today's harmonic analysis
incorporates the elements of geometric measure theory, number theory,
probability, and has countless applications from data analysis to
image recognition and from the study of sound and vibrations to the
cutting edge of contemporary physics.

The present volume is based on lectures presented at the summer
school on Harmonic Analysis. These notes give fresh, concise, and
high-level introductions to recent developments in the field, often
with new arguments not found elsewhere. The volume will be of use both
to graduate students seeking to enter the field and to senior
researchers wishing to keep up with current developments.

Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute.

#### Readership

Graduate students and researchers interested in harmonic analysis and its applications to diffusion processes and propagation of waves.

# Table of Contents

## Harmonic Analysis and Applications

Table of Contents pages: 1 2

- Cover Cover11
- Title page iii4
- Lecture notes on quantitative unique continuation for solutions of second order elliptic equations 114
- Arithmetic spectral transitions: a competition between hyperbolicity and the arithmetics of small denominators 3548
- Quantitative homogenization of elliptic operators with periodic coefficients 7386
- Stochastic homogenization of elliptic equations 131144
- 𝑇1 and 𝑇𝑏 theorems and applications 155168
- Sliding almost minimal sets and the Plateau problem 199212
- Introduction 200213
- Some Plateau problems 201214
- Almost minimal sets and what we want to do 209222
- Weak regularity properties for almost minimal sets 212225
- Limits of almost minimal sets 223236
- Monotonicity of density, near monotonicity, and blow-up limits 228241
- Minimal cones and the Jean Taylor theorem 233246
- Sliding almost minimal sets 236249
- V. Feuvrier and existence results 243256

- Almgren’s center manifold in a simple setting 257270
- Lecture notes on rectifiable Reifenberg for measures 289302

Table of Contents pages: 1 2