Hausdorff Center for Mathematics Courses

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
• On-Demand
• 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
• On-Demand
• Free Video

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
• On-Demand
• 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
• On-Demand
• Free Video

On Categorification of GKZ Hypergeometric Systems - Work in Progress

Explore the categorification of GKZ hypergeometric systems and its connection to local toric mirror symmetry through isotrivial families of triangulated categories.

• YouTube
• 1 hour
• On-Demand
• Free Video

Singularities in Fluid

Explore innovative techniques for investigating fluid singularities, including self-similar analysis, computer-assisted proofs, and neural networks.

• YouTube
• 49 minutes
• On-Demand
• Free Video

Polyhedral Techniques in Combinatorial Optimization - Matchings and Tours

Explore recent advancements in combinatorial optimization, focusing on matching and traveling salesman problems. Learn about polyhedral techniques and linear programming formulations for designing efficient algorithms.

• YouTube
• 39 minutes
• On-Demand
• Free Video

Minimal Rank of Submatrices of Random Rectangular Matrices

Explore the minimal rank of square submatrices in random rectangular matrices, proving a conjecture on their behavior as matrix dimensions vary.

• YouTube
• 40 minutes
• On-Demand
• Free Video

Floating Bodies and Duality in Spaces of Constant Curvature

Explores p-affine surface area and floating bodies in curved spaces, extending Meyer & Werner's Euclidean results to spherical and hyperbolic geometries. Examines limiting behavior as curvature approaches zero.

• YouTube
• 30 minutes
• On-Demand
• Free Video

Recent Advances in Valuations on Function Spaces

Explore recent developments in valuations on function spaces, focusing on convex and continuous functions, with insights into measure-valued valuations and their classifications.

• YouTube
• 41 minutes
• On-Demand
• Free Video

Around the Nash Problem for Smooth Valuations

Explore smooth valuations on manifolds, their relation to translation-invariant valuations, and Crofton formulas. Discover surprising flexibility properties in finite subspace families.

• YouTube
• 39 minutes
• On-Demand
• Free Video

Lefschetz Operators on Minkowski Valuations

Explore Lefschetz operators' action on continuous Minkowski valuations compatible with rigid motions, including difference body, projection body, and mean section body maps.

• YouTube
• 22 minutes
• On-Demand
• Free Video

Entropy, Isotropic Constant and Mahler's Conjecture

Explores connections between entropy, isotropic constant, and Mahler's conjecture in convex geometry. Discusses functional forms of Klartag's work and adaptations for log-concave functions.

• YouTube
• 56 minutes
• On-Demand
• Free Video

Brunn-Minkowski Inequalities for Sprays on Riemannian Surfaces

Generalization of Minkowski average on Riemannian manifolds, characterizing curve families on surfaces satisfying Brunn-Minkowski inequality. Explores conditions for constant-speed curves and geodesic curvature.

• YouTube
• 24 minutes
• On-Demand
• Free Video

Comparison Problems for the Radon Transform

Explores comparison problems for Radon transforms, examining conditions for L^p-norm inequalities and introducing function classes generalizing intersection bodies, with applications to slicing inequalities.

• YouTube
• 53 minutes
• On-Demand
• Free Video