Hausdorff Center for Mathematics Courses

Concentration Functions and Entropy Bounds for Discrete Log-Concave Distributions

Explore concentration functions and entropy bounds for discrete log-concave distributions, with applications to entropy power inequalities. Based on joint research in probability theory.

• YouTube
• 44 minutes
• Self-Paced
• Free Video

Stochastic Analysis and Geometric Functional Inequalities

Explore methods for proving functional inequalities in hypoelliptic diffusions, including geometric and probabilistic approaches, with applications to Langevin dynamics ergodicity.

• YouTube
• 56 minutes
• Self-Paced
• Free Video

Ilya Molchanov - Random Sets Generated by Translates of a Convex Body

Explores K-hulls and K-strongly convex sets, analyzing facial structures and applying theory to random point samples. Discusses convergence of f-vectors and related probabilistic results.

• YouTube
• 30 minutes
• Self-Paced
• Free Video

Peter Pivovarov- Random S-Concave Functions and Isoperimetry

Explore stochastic geometry of s-concave functions, local stochastic isoperimetry, and shadow systems. Discover functional inequalities and their applications in this advanced mathematical discussion.

• YouTube
• 29 minutes
• Self-Paced
• Free Video

Schramm-Steif Variance Inequalities for Poisson Processes and Noise Sensitivity

Explore Poisson processes, variance inequalities, and noise sensitivity in stochastic geometry. Gain insights into k-percolation and the Poisson Boolean model with bounded grains.

• YouTube
• 34 minutes
• Self-Paced
• Free Video

Facets of High Dimensional Random Polytopes

Explore asymptotic behavior of high-dimensional random polytopes, analyzing facets and their geometric properties as dimensions and data points increase, revealing insights into spherical approximations and tessellations.

• YouTube
• 30 minutes
• Self-Paced
• Free Video

Random Polytopes

Explores beta and beta' polytopes in stochastic geometry, discussing random cones, Poisson cells, and spherical objects. Examines angles and functionals of these models.

• YouTube
• 44 minutes
• Self-Paced
• Free Video

Random Polytopes II

Explore beta and beta' polytopes in stochastic geometry, including random cones, Poisson cells, and spherical objects. Learn to compute expected angles and express model functionals.

• YouTube
• 42 minutes
• Self-Paced
• Free Video

The Large Deviations Approach to High-Dimensional Convex Bodies - Lecture I

Explores large deviation principles in high-dimensional convex bodies, focusing on non-universal behaviors in random projections and their relation to underlying geometry.

• YouTube
• 51 minutes
• Self-Paced
• Free Video

Zakhar Kabluchko - Random Polytopes

Introduction to beta polytopes: convex hulls of samples from beta density on unit ball and beta' density on Euclidean space. Explores models in stochastic geometry reducible to these polytopes.

• YouTube
• 51 minutes
• Self-Paced
• Free Video

A Remark on the Minimal Dispersion

Explore improved upper bounds for minimal dispersion in unit cubes, with some results sharp to logarithmic factors. Gain insights into this mathematical concept.

• YouTube
• 59 minutes
• Self-Paced
• Free Video

Random Tessellations in Hyperbolic Space - First Steps

Explore random tessellations in hyperbolic space, focusing on Poisson hyperplane tessellations and their unique dimension-dependent phenomena compared to Euclidean and spherical spaces.

• YouTube
• 1 hour
• Self-Paced
• Free Video

An Overview on a Young Research Topic - Valuations on Spaces of Functions

Explore valuations on function spaces, from convex bodies to Lipschitz and convex functions. Learn about recent classifications and advancements in this emerging mathematical field.

• YouTube
• 51 minutes
• Self-Paced
• Free Video

The Mysterious Extremals of the Alexandrov-Fenchel Inequality

Explore the Alexandrov-Fenchel inequality's extremal bodies, recent progress in characterizing them for convex polytopes, and insights into this fundamental problem in convex geometry.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

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.

• YouTube
• 49 minutes
• Self-Paced
• Free Video