Hausdorff Center for Mathematics Courses

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

Monica Vazirani- Representations of the Affine BMW Category

Explore Walker's TQFT-motivated construction of affine BMW category representations, their combinatorial description, and implications for affine BMW algebra representations in this advanced mathematics lecture.

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

Tautological p-Kazhdan-Lusztig Theory for Cyclotomic Hecke Algebras

Explores isomorphism between quiver Hecke algebras and diagrammatic endomorphism algebras, proving equality of decomposition numbers and p-Kazhdan-Lusztig polynomials for cyclotomic Hecke algebras.

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

Felix Klein Lectures 2020: Quiver Moduli and Applications

Explore quiver moduli spaces' topology, geometry, and cohomology. Discover applications in Gromov-Witten and Donaldson-Thomas theory through wall-crossing techniques in advanced algebraic geometry.

• YouTube
• 1 hour 13 minutes
• Self-Paced
• Free Video