Hausdorff Center for Mathematics Courses

On the Classification of Compactified Jacobians of Nodal Curves

Explore modular degenerations of Jacobians when smooth curves become nodal, with insights from recent Pagani-Tommasi findings in algebraic geometry.

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

Derived Deformations of Crepant Curves

Explore advanced algebraic geometry concepts, focusing on (-3,1)-curves in CY 3-folds and their noncommutative deformation theory, with applications to string theory predictions.

• YouTube
• 56 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

Jason Miller- Conformal Removability of SLEκ for κ∈[4,8)

Explores conformal removability of SLEκ curves, focusing on κ=4. Presents new conditions for conformal removability and discusses applications to SLEκ for κ∈(4,8). No prior SLE or LQG knowledge required.

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

Marie-France Vigneras - Representations of GLn(D) Near the Identity

Explore representations of general linear groups over p-adic fields, focusing on dimension formulas for fixed points under congruence subgroups and extensions to inner forms.

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

J. E. Rodriguez Camargo: A Local Jacquet-Langlands Correspondence for Locally Analytic D-Modules

Explore an equivalence between GL₂(F)-equivariant D-modules on Drinfeld space and D*^-equivariant D-modules on P¹, with applications to Scholze's functor and admissible representations.

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

A Fourier Transform for Abelian Fibrations

Explore Fourier transform theory for abelian fibrations, extending Beauville decomposition and examining perverse filtration applications in algebraic geometry and motivic theory.

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

Filling a Few Holes in the Classical Resolution of Singularities

Exploring new discoveries in resolution of singularities, challenging the notion of a completed field and providing a unified view on recent advancements in characteristic zero mathematics.

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

Osamu Fujino- Minimal Model Program for Projective Morphisms Between Complex Analytic Spaces

Explore advanced algebraic geometry concepts, focusing on minimal model program for projective morphisms between complex analytic spaces, extending results to new contexts.

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

Derived Microlocal Geometry and Virtual Invariants

Explore derived microlocal geometry and its application to virtual invariants, including a 3D refinement of the 2D cohomological Hall algebra in this advanced mathematics lecture.

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

On the Smoothing Problem for Cycles in the Whitney Range

Explores cycle smoothability in algebraic geometry, focusing on the Whitney range. Presents new results and conjectures on constructing cycles from products of divisors.

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Free Video

Cinzia Casagrande- Fano 4-Folds With B2 Greater Than 12 Are Products of Surfaces

Explore complex Fano 4-folds and their properties, focusing on the relationship between second Betti numbers and surface products in algebraic geometry.

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

Stability and Learning in Strategic Games

Explores strategic user behavior in games, focusing on traffic routing and online auctions. Discusses recent developments in repeated games with carry-over effects, particularly in queuing systems.

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

Boolean Models in Hyperbolic Space

Explore Boolean models in hyperbolic space, examining geometric functionals and asymptotic formulas for expectations, variances, and covariances, with insights into new phenomena compared to Euclidean cases.

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