Hausdorff Center for Mathematics Courses

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
• Self-Paced
• Free Video

Complex Surfaces With Many Algebraic Structures

Explore complex surfaces with multiple algebraic structures through blowups, elliptic curves, and Hopf transforms. Discover new insights in algebraic geometry and complex analysis.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video

Resonance and Koszul Modules

Explore resonance varieties in algebraic settings, examining their structure and applications to vector bundles, moduli, Koehler groups, and hyperplane arrangements.

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Free Video

Mauro Varesco- Degenerations of Type III

Explore degenerations of Type III with Mauro Varesco, delving into advanced mathematical concepts and their applications in algebraic geometry and related fields.

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

Query Lower Bounds for Log-Concave Sampling

Explores complexity lower bounds for sampling from log-concave distributions, using modified Perron's sprouting construction for Kakeya sets to establish tight bounds in low dimensions.

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

Isoperimetric Problem- From Classical to Reverse I

Explore the classical isoperimetric problem and its reverse, focusing on minimizing volume for convex bodies with bounded curvature. Learn about recent developments in R3.

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

Isoperimetric Problem- From Classical to Reverse II

Explore the reverse isoperimetric problem for convex bodies with bounded curvature, focusing on volume minimization in R3 and its implications for geometric analysis.

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

The Floating Body Construction and Its Applications

Explore the floating body construction in geometry, its properties, and applications in affine surface area and random polytopes. Discover generalizations to non-Euclidean spaces.

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

Critical Intersection Volumes of -Schatten- P-Balls

Explores critical thresholds in high-dimensional geometry, focusing on intersection volumes of unit-volume balls and their limiting distributions, with applications to classical and Schatten p-balls.

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

Isoperimetric Problem - From Classical to Reverse III

Explores the reverse isoperimetric problem for convex bodies with bounded curvature, focusing on volume minimization in R3 and its implications for geometric analysis.

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

David Steigenberger: Random Beta Simplices and Parallelotopes

Explore random simplices and parallelotopes in geometry, focusing on beta-distributed vectors. Learn about volume calculations and distributional representations using geometric approaches.

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

Extremizers in Fenchel and Bezout-Type Inequalities

Exploration of affine invariant ratios in mixed volumes, focusing on minimizers and maximizers in Fenchel and Bezout-type inequalities. Discusses open problems and characterizations of geometric shapes.

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

Connections Between Minimal Norm Interpolation and Local Theory of Banach Spaces

Explores statistical performance of minimum norm interpolators in non-linear regression, focusing on 2-uniformly convex norms and cotype 2 property. Analyzes bias and variance using tools from Banach space theory.

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

Formalizing Infinity-Category Theory in the Rzk Proof Assistant

Explore the formalization of ∞-category theory using the Rzk proof assistant, delving into advanced mathematical concepts and their computational representations.

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