Hausdorff Center for Mathematics Courses

Mauro Varesco- Degenerations of Type III

Explore degenerations of Type III with Mauro Varesco, delving into advanced mathematical concepts and their applications in algebraic geometry and related fields.

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

Probabilistic Methods in Hyperbolic Geometry

Explore probabilistic approaches to solve geometric and topological questions in hyperbolic manifolds, bridging mathematics domains through innovative analytical techniques.

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

Mira Gordin: Vector-Valued Concentration on the Symmetric Group

Explore vector-valued concentration inequalities on the symmetric group, their implications for Banach space embeddings, and connections to metric geometry and algorithmic applications.

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

Variational Functionals in the Gauss Space

Explore variational functionals in Gauss space, examining electrostatic capacity, torsion, and Dirichlet eigenvalue. Investigate Brunn-Minkowski inequalities and Hadamard formulas in Convex Geometry.

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

Local Uniqueness Results for Centroid Bodies

Explore local uniqueness of centroid bodies through hyperplane conditions, examining volume, area, inertia, and distance properties to determine if specific combinations imply a Euclidean ball shape.

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

Fiber Symmetrization in the Space of Matrices

Explore fiber symmetrization in matrix spaces, its properties, and applications to isoperimetric inequalities for convex bodies, generalizing Steiner symmetrization to higher dimensions.

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

Dylan Langharst: Higher-Order Affine Isoperimetric Inequalities

Explores extensions of geometric inequalities to higher-order bodies, including projection, centroid, LYZ, and radial mean bodies, with proofs of associated inequalities in convex geometry.

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

Geometric Functional Inequalities, Old and New

Explore geometric functional inequalities as convexity statements, linking Ehrhard's and Bobkov's inequalities, and discover new generalizations in this insightful mathematical lecture.

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

Central Limit Theorems for Poisson Functionals - The Malliavin-Stein Approach

Explore central limit theorems in stochastic geometry using the Malliavin-Stein method, with applications to random point collections and the Online Nearest Neighbour Graph.

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

The Functional Volume Product Under Heat Flow

Explores monotonicity of functional volume product along Fokker-Planck heat flow, leading to improved Borell's hypercontractivity and Laplace transform quasi-norm lower bound.

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