Hausdorff Center for Mathematics Courses

Categorical Aspects of the KSB Correspondence I

Exploring M-resolutions, N-resolutions, and the KSB correspondence for cyclic quotient singularities, with insights on MMP-induced braid group actions and applications to Dolgachev surfaces.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

Generic Prym-Torelli Theorem for Cyclic Coverings of Genus 2 Curves

Explore cyclic unramified coverings of genus 2 curves and their associated Prym varieties, focusing on the injectivity of the Prym map for Sophie Germain prime degree coverings.

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

Intersection Theory and the Mandelbrot Set

Explores the Mandelbrot set's connections to arithmetic intersection theory, revealing new insights into this complex mathematical object. Joint work with Myrto Mavraki.

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

Martin Hairer - Stochastic Quantisation of Yang-Mills

Explores recent progress in constructing a stochastic process with Yang-Mills measure as its invariant measure, focusing on gauge-covariance preservation despite UV regularization breaking.

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

From Phase Separation in Heterogeneous Media to Learning Training Schemes for Image Denoising

Exploring variational approaches in phase separation and image denoising, focusing on heterogeneous media, geometric measure theory, and optimized training schemes for improved performance.

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

String Topology of Finite Groups of Lie Type

Explore string topology's role in understanding cohomology of finite Lie-type groups, connecting to loop spaces and algebraic geometry. Gain insights into recent developments in this mathematical field.

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

Jacob Lurie: A Riemann-Hilbert Correspondence in P-adic Geometry

Explore p-adic geometry and the Riemann-Hilbert correspondence, covering perfectoid spaces, crystals, and spectral methods in this advanced mathematics lecture.

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

The Module Structure of a Group Action on a Ring

Explore finite group actions on graded algebras, examining module multiplicities and their connections to homological algebra and geometric group actions.

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

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