Hausdorff Center for Mathematics Courses

The Balmer Spectrum of Cellular C-Motivic Spectra

Exploration of the Balmer spectrum in cellular C-motivic spectra, focusing on its periodicity (co)sheaf and the C2 group action on formal groups through the [−1]-series.

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

An Introduction to Chromatic Homotopy Theory

Explore Morava K-theories, E-theories, and their role in chromatic homotopy theory. Delve into K(n)-local categories and the connection between E-theory and group cohomology.

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

Tensor Triangular Geometry - Lecture 1

Explore symmetric monoidal triangulated categories, their spectra, and analogies to algebraic geometry. Delve into challenges in compactly generated settings and tensor triangulated fields.

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

Thomas Nikolaus- K-Theory of Z-P^n and Relative Prismatic Cohomology

Explore K-theory computation for Z/p^n rings using prisms and prismatic cohomology. Learn about generalized prisms and their universal property in this advanced mathematical discussion.

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

Brent Nelson- Free Stein Dimension

Explore free Stein dimension in tracial von Neumann algebras, its computation, and implications for structural properties of von Neumann algebras.

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

A Farrell-Jones Isomorphism for Scissors Congruence K-Theory

Explore a new trace map in scissors congruence K-theory, its refinement, and its role in proving the Farrell-Jones isomorphism. Joint work with Mona Merling and Inna Zakharevich.

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

Hammond and Sheffields Power Law Pólya's Urn

Explores power law Pólya's urn model, analyzing genealogical aspects, coalescence probabilities, and asymptotic behavior. Discusses random partitions, fractional Brownian motion, and metastable systems in probability theory.

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

Vortrag "Wo steht die mathematische Forschung?"

Einblick in aktuelle mathematische Forschung anhand der Riemannschen Vermutung. Experten erläutern zentrale Ideen und Fortschritte der letzten 100 Jahre zu diesem berühmten ungelösten Millenniumsproblem.

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

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