Isoperimetric and Poincaré Inequalities on the Hamming Cube
Explore isoperimetric inequalities on the Hamming cube near and at the critical exponent 1/2, as well as closely related L1 Poincaré inequalities in this one-hour lecture. Delve into joint research conducted with P. Durcik and P. Ivanisvili, focusing on…
Dirichlet-to-Neumann Map for the p-Laplacian on Metric Measure Spaces
Explore the Dirichlet-to-Neumann map for p-Laplacian on metric measure spaces. Delve into Newton-Sobolev spaces, trace classes, and Besov functions in the context of Dirichlet and Neumann problems.
Random Graphs and Nonlinear Spectral Gaps
Explore discrete Poincaré inequalities in regular expander graphs, long-range expansion properties, and their implications for Banach space-valued functions, with improved estimates for Poincaré constants.
On Chen’s Recent Breakthrough on the Kannan-Lovasz-Simonovits Conjecture and Bourgain's Slicing Problem - Part III
Explore Chen's breakthrough on the KLS conjecture and Bourgain's slicing problem, covering key mathematical concepts, historical context, and implications for discrete mathematics and computer science.
Alexander Volberg - Poincaré Inequalities on Hamming Cube - Analysis, Combinatorics, Probability
Explore improved L^1-Poincaré inequality constants on Hamming cube, comparing with Gaussian space. Discuss proofs, estimates, and related mathematical concepts in analysis, combinatorics, and probability theory.
Functional Inequalities and Concentration of Measure I
Explore concentration inequalities in probability and geometric analysis, focusing on functional inequalities and their applications to Lipschitz functions in continuous and discrete settings.
Functional Inequalities and Concentration of Measure III
Explores concentration inequalities in probability and geometric analysis, focusing on functional inequalities like Poincaré and log-Sobolev. Covers properties, applications to Lipschitz functions, and various measure settings.
Functional Inequalities and Concentration of Measure II
Explores concentration inequalities in probability and geometric analysis, focusing on functional inequalities like Poincaré and log-Sobolev. Covers properties, applications to Lipschitz functions, and various measure settings.
Looking for p-Energy Forms in Cheeger Spaces
Explore p-energy forms in Cheeger spaces without relying on gradients. Learn about constructing these forms using characteristic features of Cheeger metric measure spaces.
Uniform Volume Doubling and Functional Inequalities on Lie Groups
Explore functional inequalities on Lie groups, focusing on uniform volume doubling and its implications for SU(2) and related structures. Gain insights into heat kernel estimates and measure contracting properties.
Spectral Gap Estimates for the Random Field Ising Model - Lecture
Spectral gap estimates for random field Ising model: convergence rates, Glauber dynamics, Griffiths phase. Combines stochastic localization and percolation-theoretic coarse-graining techniques.
Quantum Gibbs Samplers: Simulation and Convergence Analysis
Delve into quantum Gibbs sampling through Lindblad dynamics, exploring efficient sampling methods and convergence properties in open quantum systems.
On Gilles Pisier's Approach to Gaussian Concentration, Isoperimetry, and Poincare-Type Inequalities
Explore advanced mathematical concepts in measure concentration, isoperimetry, and Poincaré-type inequalities through Pisier's approach and its extensions to rotationally invariant distributions.