Hausdorff Center for Mathematics Courses

David Bate: On 1-Regular and 1-Uniform Metric Measure Spaces

Explore 1-regular and 1-uniform metric measure spaces with David Bate, delving into advanced mathematical concepts and their applications in geometric measure theory.

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

Jonathan Hickman- On Littlewood-Paley Theory for Space Curves

Explore Littlewood-Paley inequalities for functions with Fourier transforms near submanifolds, focusing on space curves and applications in harmonic analysis, PDE, and number theory.

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

Fubini-Type Theorems for Hausdorff Dimension and Their Connection to Unions of Lines

Explore Fubini-type theorems for Hausdorff dimension and their relationship to unions of lines, gaining insights into advanced mathematical concepts and their applications.

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

Boundary Unique Continuation and the Estimate of the Singular Set

Explore boundary unique continuation for harmonic functions and its application in estimating singular sets of elliptic PDEs. Gain insights into local growth rates and their global implications in mathematical analysis.

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

The Regularity Problem for the Laplace Equation in Rough Domains

Explores recent advances in Boundary Value Problems for the Laplace operator in rough domains, focusing on the equivalence between Dirichlet and regularity problem solvability.

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

José María Martell - Layer Potentials, Extrapolation and Boundary Value Problems in Unbounded Domains

Explore layer potentials, extrapolation, and boundary value problems in unbounded domains. Learn about elliptic systems, Neumann series, and weighted Banach function spaces in this advanced mathematics lecture.

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

Discrete Minimizers of Energy Integrals

Explore the intriguing phenomenon of discrete minimizers in energy integral optimization, its counterintuitive nature, and applications in various fields of mathematics and signal processing.

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

Moving Currents - On the Lie Transport Equation and a Rademacher Type Theorem

Explore the Lie transport equation for k-currents, extending classical transport theory to generalized surfaces. Insights on challenges and recent developments in modeling defects in plastic materials.

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

Distance Sets Spanned by Sets of Dimension D/2

Explores distance sets in R^d, proving theorems on Hausdorff and packing dimensions. Analyzes relationships between set dimensions and their distance sets, with focus on d/2 dimension cases.

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

On Extremizers for Fourier Restriction onto the Moment Curve

Explore Fourier restriction/extension operators for moment curves, focusing on functions that maximize operator norms in Lebesgue spaces. Recent findings with Betsy Stovall discussed.

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

Guido De Philippis - PDE Constrained Measures III

Explore advanced concepts in PDE-constrained measures with Guido De Philippis, delving into complex mathematical theories and applications in this advanced lecture.

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

Steve Hofmann - Quantitative Rectiability, and Harmonic and Caloric Measure III

Explore advanced mathematical concepts in quantitative rectifiability and measure theory, focusing on harmonic and caloric measures in complex analytical settings.

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

Frequency Function Methods in PDE I

Explore frequency function methods in partial differential equations, focusing on applications and theoretical foundations for solving complex mathematical problems.

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

PDE Constrained Measures I

Explore PDE constrained measures with Guido De Philippis in this advanced mathematical lecture, delving into complex analytical concepts and their applications.

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

Recent Hardness of Approximation Results in Parameterized Complexity

Survey of recent hardness of approximation results in parameterized complexity, focusing on k-clique problem inapproximability, with technical insights and open problems discussion.

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