Hausdorff Center for Mathematics Courses

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

LP-Norm Multiway Cut

Explores graph partitioning with lp-norm multiway cut, unifying min-sum and min-max variants. Discusses hardness, integrality gap, and approximation algorithm for this generalized problem.

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

Generalized Permutahedra and Optimal Auctions

Explore SIM-bodies as generalized permutahedra, their role in Straight-Jacket Auctions, and the application of computer algebra for determining optimal prices and revenues in auction theory.

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

Noriyoshi Sukegawa- On the Diameter of Polyhedra and Related Topics

Explore polyhedra diameter and its impact on simplex method complexity. Overview previous findings, recent results, and open questions in this mathematical field.

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