Hausdorff Center for Mathematics Courses

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

Mixed Integer Optimization in High Dimensions

Explore advanced techniques for solving high-dimensional mixed integer optimization problems, focusing on cutting-edge algorithms and theoretical foundations.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

Parameterized Problems Complete for Nondeterministic FPT Time and Logarithmic Space

Exploration of XNLP-complete problems in parameterized complexity, including List Coloring, Scheduling, Bandwidth, and CNF-Satisfiability variants, with implications for W[t]-hardness and long-standing questions.

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

Parametrized Algorithms and Possible Future Directions

Explore current research and future directions in Parameterized Complexity, focusing on algorithmic approaches and potential areas for further investigation.

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

The Approximation Ratio of the k-Opt Heuristic for Euclidean TSP

Explore the k-Opt heuristic's approximation ratio for Euclidean TSP, improving upper bounds and providing new lower bounds for k ≥ 3, applicable to various p-norms.

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