Hausdorff Center for Mathematics Courses

Hard Lefschetz Theorem and Hodge-Riemann Relations for Convex Valuations

Explore mixed hard Lefschetz theorem and Hodge-Riemann relations in smooth valuations, generalizing Alexandrov-Fenchel inequality for convex bodies using operator perturbation theory.

• YouTube
• 51 minutes
• On-Demand
• Free Video

Rademacher Projection in Non-Symmetric Convex Bodies - Alexander Litvak

Explores the Rademacher projection in non-symmetric convex bodies, proving sharpness of bounds and discussing implications for Banach-Mazur distances and mean zero functions.

• YouTube
• 56 minutes
• On-Demand
• Free Video

Random Tessellation Forests: Overcoming the Curse of Dimensionality

Explore random tessellation forests in machine learning, overcoming dimensionality challenges through innovative partitioning methods and directional distributions for improved statistical performance.

• YouTube
• 58 minutes
• On-Demand
• Free Video

Boolean Models in Hyperbolic Space

Explore geometric functionals of Boolean models in hyperbolic space, examining volume intersections, asymptotic behaviors, and statistical properties, revealing unique phenomena compared to Euclidean counterparts.

• YouTube
• 49 minutes
• On-Demand
• Free Video

Brunn-Minkowski Inequalities via Concavity of Entropy

Explore Brunn-Minkowski inequalities through the lens of entropy concavity, gaining insights into geometric and functional analysis concepts.

• YouTube
• 27 minutes
• On-Demand
• Free Video

Kubota-Type Formulas and Supports of Mixed Measures

Explores mixed surface area measures and Kubota-type formulas for convex functions, addressing Schneider's conjecture and applications to Monge-Ampère measures.

• YouTube
• 23 minutes
• On-Demand
• Free Video

Vysotskiy - The Isoperimetric Problem for Convex Hulls and the Large Deviations Rate Functions

Explores large deviations principle for convex hull areas in planar random walks, analyzing optimal trajectories and solving the Euler-Lagrange equation for various rate functions.

• YouTube
• 28 minutes
• On-Demand
• Free Video

Two-Sided Estimates for Operator ℓp to ℓq Norms of Random Matrices with IID Entries

Explore two-sided estimates for operator norms of random matrices, discussing proofs, examples, and open problems in this mathematical analysis of iid entries and their implications.

• YouTube
• 23 minutes
• On-Demand
• Free Video

Limit Theorems for the Volumes of Small Codimensional Random Sections of Lpn-Balls

Explore central limit theorems for volumes of random sections in high-dimensional geometry, with insights on open questions and recent research developments.

• YouTube
• 54 minutes
• On-Demand
• Free Video

The Aleksandrov Projection Theorem for Convex Lattice Polygons

Explore the discrete analogue of Aleksandrov's projection theorem for convex lattice polygons, examining counterexamples and their implications in Z^2.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Concentration Inequalities for Poisson U-Statistics

Explore concentration inequalities for Poisson U-statistics, their optimality, and applications in stochastic geometry models. Gain insights into Poisson functionals and their significance in geometric analysis.

• YouTube
• 49 minutes
• On-Demand
• Free Video

Large Deviations Principle for Sub-Riemannian Random Walks

Explore large deviations in sub-Riemannian random walks on Carnot groups, focusing on rate functions, hypoelliptic Brownian motions, and comparisons between standard and Heisenberg group Brownian motions.

• YouTube
• 1 hour
• On-Demand
• Free Video

Extension Complexity of Random Polytopes

Explores extension complexity of random polytopes, discussing results for fixed-dimension convex hulls of random points on unit sphere or ball. Joint work with Kwan and Zhao.

• YouTube
• 46 minutes
• On-Demand
• Free Video

Boolean Models in Hyperbolic Space

Explore Boolean models in hyperbolic space, examining geometric functionals and asymptotic formulas for expectations, variances, and covariances, with insights into new phenomena compared to Euclidean cases.

• YouTube
• 26 minutes
• On-Demand
• Free Video

Fluctuations of Linear Eigenvalue Statistics in Sample Covariance Matrices - Tensor Product Data

Explore fluctuations in linear eigenvalue statistics of sample covariance matrices with tensor product data, comparing normal and uniform distributions on unit sphere.

• YouTube
• 56 minutes
• On-Demand
• Free Video