Hausdorff Center for Mathematics Courses

Vortrag "Was lehrt uns die Geschichte über mathematische Probleme?"

Historische Perspektive auf ungelöste mathematische Probleme: Einblicke in die Entwicklung und Bedeutung der Millennium-Probleme, insbesondere der Riemannschen Vermutung, für Laien und Mathematikinteressierte.

• YouTube
• 1 hour 11 minutes
• Self-Paced
• Free Video

Sind Primzahlen dem Zufall unterworfen?

Einführung in die faszinierende Welt der Arithmetik und die Riemannsche Vermutung. Erläuterung der Bedeutung von Primzahlen und ihrer Verteilung, sowie die Relevanz dieses Millenniumsproblems für die Mathematik und darüber hinaus.

• YouTube
• 1 hour 36 minutes
• Self-Paced
• Free Video

Justifiable Quantum Advantage for Stylized Learning Challenges

Explore quantum advantage in learning tasks, demonstrating how quantum machines can predict physical properties and model dynamics with exponentially fewer experiments than conventional methods.

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

Formalisierung der Mathematik - Wann führen Computer die Beweise?

Experten diskutieren die Zukunft formaler mathematischer Beweise durch Computer, deren Potenzial, Herausforderungen und Auswirkungen auf die mathematische Forschung und Gemeinschaft.

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

Helmut Bölcskei - Lossy Compression on General Data Structures

Explore lossy compression for data on manifolds and fractals, with bounds on rate-distortion function and quantization error. Applications in data science and image processing.

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

Kathlén Kohn - The Geometry of Linear Convolutional Networks

Explore the geometry of linear convolutional networks, their function spaces, and optimization challenges. Gain insights into critical points, polynomial representations, and architectural impacts.

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

Solving Inverse Problems With Deep Neural Networks - Robustness Included?

Exploring robustness of deep learning in inverse problems, focusing on resilience against statistical noise and adversarial perturbations in image reconstruction tasks.

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

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

Green Function vs. Geometry

Explore the relationship between Green functions and geometry in higher dimensions, focusing on regular sets and elliptic operators in mathematical analysis.

• YouTube
• 48 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