Proving Analytic Inequalities

Explore the intricacies of proving analytic inequalities in this 54-minute conference talk delivered by Avi Wigderson at the 2018 Joint Mathematics Meetings. Delve into the fundamental concepts, starting with an introduction to analytic inequalities and progressing through a comprehensive syllabus. Examine the basic template, notation, and key inequalities such as Cauchy-Schwarz and Loomis-Whitney. Investigate the Young Inequality, its general form, and special cases. Discover geometric inequalities related to polytopes, matrices, and matroid intersections. Gain insights into optimal constants and general matching principles. Conclude with a summary and engage in a thought-provoking question-and-answer session to deepen your understanding of this complex mathematical topic.

Introduction
What are analytic inequalities
Basic template
Notation
Cauchy Schwarz Inequality
Loomis Whitney Inequality
Young Inequality
General Form
Less than infinity
Optimal constant
Special case
Geometric Inequalities
Polytopes
Matrix
Metroid intersection
General matching
Summary
Questions