On Chen’s Recent Breakthrough on the Kannan-Lovasz-Simonovits Conjecture and Bourgain's Slicing Problem - Part III

Delve into the third part of a comprehensive seminar exploring Chen's groundbreaking work on the Kannan-Lovasz-Simonovits conjecture and Bourgain's slicing problem. Join Ronen Eldan from the Weizmann Institute of Science as he guides you through advanced topics in computer science and discrete mathematics. Explore the intricacies of stochastic processes, martingales, and upper bounds, while gaining insights into the historical context of these mathematical challenges. Examine complex concepts such as operator norms, tensors, covariance matrices, and quadratic variation. Discover the applications of stochastic localization and investigate eigenvalues as functions. Uncover the principles behind continuous functions, repulsion, and the St Potential. Gain a deeper understanding of Dyson Brownian Motion and the Lagrange Theorem. Conclude with a discussion on the Poincare inequality, tying together the seminar's key concepts and their implications for the field.

Introduction
Properties of the process
Martingale
A small calculation
The upper bound
The history
The operator norm
Tensors
Covariance matrix
Quadratic variation
Other uses of stochastic localization
Eigenvalues as functions
Continuous functions
General lemma
Repulsion
St Potential
Dyson Brownian Motion
Lagrange Theorem
Final conclusion
Poincare inequality