Mathematics Subject Classification (2010) 35A99, 35B44, 35B65, 35Q30, 76D05

CONTENTS

1. INTRODUCTION

2. WEAK CONCENTRATION

4. STRONG CONCENTRATION

5. THREE FACETS OF QUANTITATIVE REGULARITY  

6. A GENERAL STRATEGY FOR QUANTITATIVE ESTIMATES OF DISSIPATIVE SCALES

7. QUANTITATIVE REGULARITY IN THE TYPE I CASE  

8. SOME FURTHER DEVELOPMENTS

9. MILD CRITICALITY BREAKING AND A CONJECTURE OF TAO

10. SUMMARY OF SELECTED RESULTS