Hausdorff Center for Mathematics Courses

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

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

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

Rademacher Projection in Non-Symmetric Convex Bodies - Alexander Litvak

Explores the Rademacher projection in non-symmetric convex bodies, proving sharpness of bounds and discussing implications for Banach-Mazur distances and mean zero functions.

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

Boolean Models in Hyperbolic Space

Explore geometric functionals of Boolean models in hyperbolic space, examining volume intersections, asymptotic behaviors, and statistical properties, revealing unique phenomena compared to Euclidean counterparts.

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

A New Case of BSD Conjecture and Deformation of Line Bundles

Explores a new case of the BSD conjecture for elliptic curves and examines deformation of line bundles in positive and mixed characteristic, applying rigidity properties of variations of Hodge structures.

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

Orbifold Fundamental Groups of Log Calabi-Yau Surface Pairs, and the Jordan Constant

Explores orbifold fundamental groups of log Calabi-Yau surface pairs, discussing their properties, structure, and connections to other mathematical concepts in algebraic geometry.

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

Weighted Blowups, Wall-Crossing and Weak Factorization

Explore stack-theoretic weighted blowups and their applications in resolution of singularities, destackification, wall-crossings, and weak factorization for more natural and efficient algorithms.

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

Brill-Noether Reconstruction for Fano Threefolds and Applications

Explore Brill-Noether reconstruction for Fano threefolds, focusing on Kuznetsov components and Bridgeland moduli spaces. Learn about applications in categorical Torelli theorems and auto-equivalences.

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

Stéphane Druel: Codimension 1 Foliations with Projectively Flat Tangent Bundle

Explore complex projective manifolds and codimension 1 foliations, focusing on numerically projectively flat tangent bundles and new findings on normal bundles of regular foliations.

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

Brunn-Minkowski Inequalities via Concavity of Entropy

Explore Brunn-Minkowski inequalities through the lens of entropy concavity, gaining insights into geometric and functional analysis concepts.

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

Kubota-Type Formulas and Supports of Mixed Measures

Explores mixed surface area measures and Kubota-type formulas for convex functions, addressing Schneider's conjecture and applications to Monge-Ampère measures.

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

Vysotskiy - The Isoperimetric Problem for Convex Hulls and the Large Deviations Rate Functions

Explores large deviations principle for convex hull areas in planar random walks, analyzing optimal trajectories and solving the Euler-Lagrange equation for various rate functions.

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