Hausdorff Center for Mathematics Courses

Sharp Examples for Decoupling and Related Questions

Explore open questions in decoupling, examining sharp examples and their connections to number theory and harmonic analysis. Gain insights into current challenges in the field.

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

Applications of Sharp Large Deviation Estimates in Asymptotic Convex Geometry

Explore sharp large deviation estimates in asymptotic convex geometry, including applications to random projections, norms, and volumes of Orlicz balls. Gain insights from recent research developments.

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

Some Comments on the Fundamental Gap of the Dirichlet Laplacian in Hyperbolic Space

Explore the fundamental gap of convex domains in hyperbolic space, comparing it with Euclidean space and examining different types of convexity in this advanced mathematical analysis.

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

Random Graph Matching with Improved Noise Robustness

Explores a new algorithm for exact matching of correlated Erdos-Renyi graphs, improving noise robustness in graph matching for applications in computer vision and biology.

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

On Bodies Floating in Equilibrium in Every Direction

Explore Ulam's Problem 19 on floating solids, examining historical and contemporary findings related to uniform density objects and their buoyancy properties.

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

One More Proof of the Alexandrov-Fenchel Inequality

Explore a concise proof of the Alexandrov-Fenchel inequalities for mixed volumes of convex bodies, presented by Bo'az Klartag in collaboration with other mathematicians.

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

Intrinsic Volumes on Pseudo-Riemannian Manifolds

Explore intrinsic volumes in pseudo-Riemannian geometry, covering Hadwiger's theorem, Weyl's principle, and Crofton formulas. Learn about recent developments in this advanced mathematical field.

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

Blaschke–Santaló Inequalities for Minkowski and Asplund Endomorphisms

Explores new isoperimetric inequalities for monotone Minkowski endomorphisms, extending to Asplund endomorphisms of log-concave functions, generalizing the Blaschke–Santaló inequality in convex geometric analysis.

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

On the Gaussian Minkowski Problem

Explore the Minkowski problem for Gaussian surface area measure, examining uniqueness and existence results in this collaborative research presentation.

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

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