Hausdorff Center for Mathematics Courses

Gaussian Isoperimetry and Related Topics III

Explore Gaussian isoperimetry's applications in probability and analysis, including concentration inequalities, noise stability, and Sobolev-type inequalities. Learn proof methods from geometric measure theory.

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

Some Applications of Variational Techniques in Stochastic Geometry III

Explores probabilistic bounds on Poisson space, measuring Gaussian distance for two-scale stabilization elements. Discusses quantitative CLTs for weakly stabilizing functionals and novel bounds for strongly stabilizing ones.

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

Some Applications of Variational Techniques in Stochastic Geometry II

Explore second-order Poincaré inequalities on the Poisson space and their geometric applications, focusing on quantitative CLTs and fourth-moment theorems in stochastic geometry.

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

Functional Inequalities and Concentration of Measure II

Explores concentration inequalities in probability and geometric analysis, focusing on functional inequalities like Poincaré and log-Sobolev. Covers properties, applications to Lipschitz functions, and various measure settings.

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

Gaussian Isoperimetry and Related Topics II

Explore Gaussian isoperimetry's applications in probability and analysis, including concentration inequalities, noise stability, and Sobolev-type inequalities. Learn proof methods from geometric measure theory.

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

On Yuansi Chen's Work on the KLS Conjecture II

Explores recent progress on the KLS conjecture in high-dimensional geometry, focusing on Yuansi Chen's work and Eldan's Stochastic Localization technique. Discusses implications for Bourgain's slicing problem.

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

Geometric Probabilities and Valuation Theory

Explore applications of geometric valuation theory to probabilities and integral geometry, including Cauchy-Kubota formulas and recent findings for convex functions.

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

Gaussian Isoperimetry and Related Topics I

Explore Gaussian isoperimetry's applications in probability and analysis, including concentration inequalities, noise stability, and Sobolev-type inequalities. Learn proof techniques using geometric measure theory.

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

Categorifying Hecke Algebras at Prime Roots of Unity

Explore advanced algebraic techniques for categorifying Hecke algebras at prime roots of unity, utilizing p-DG categories in this cutting-edge mathematical research presentation.

• YouTube
• 1 hour 9 minutes
• Self-Paced
• Free Video

Mikhail Khovanov: Universal Construction in Ultra Low Dimensions

Explore the universal construction concept as a relaxation of TQFT axioms, with applications in one and two-dimensional spaces.

• YouTube
• 1 hour 8 minutes
• Self-Paced
• Free Video

Martina Lanini- Attractive Forests and Torus Actions

Explore quiver representations, torus actions on quiver Grassmannians, and their applications in algebraic geometry, focusing on attractive forests and nilpotent representations of equioriented cycles.

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

Two Dimensional Topological Field Theories and Partial Fractions

Explore the connection between 2D topological field theories and sequences derived from surface evaluations, examining target category impacts on sequence occurrence.

• YouTube
• 1 hour 9 minutes
• Self-Paced
• Free Video

Modular Perverse Sheaves on the Affine Flag Variety

Explore geometric representation theory, focusing on categorical realizations of the affine Hecke algebra and the challenge of relating constructible and coherent sheaves through category equivalence in modular cases.

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

Soergel Bimodules and the Carlsson-Mellit Algebra

Explores categorical analogues of symmetric functions, focusing on Soergel bimodules and their connection to the Carlsson-Mellit algebra action in algebraic topology and representation theory.

• YouTube
• 1 hour 7 minutes
• Self-Paced
• Free Video

A Categorified Double Centraliser Theorem and Applications to Soergel Bimodules

Explore advanced representation theory concepts, including categorified double centraliser theorem and its applications to Soergel bimodules in finite Coxeter type and characteristic zero.

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