Convex Geometry Courses and Certifications

Hausdorff Center for Mathematics

The Convex Geometry of Blind Deconvolution and Matrix Completion Revisited

Explores convex geometry in blind deconvolution and matrix completion, analyzing dimensional factors in noise bounds and proposing alternative error scaling approaches for low-rank matrix recovery problems.

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

BIMSA

Around the Alexandrov-Fenchel Inequality - Convex Geometry and Its Applications

Explore the history and recent progress in convex geometry, focusing on Minkowski's theory and its connections to various mathematical disciplines.

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

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

The Funk Metric in Convex Geometry and Related Fields

Explore the Funk metric's connections to convex geometry, affine geometry, and combinatorics. Discover its projective invariance and relations to various conjectures and theorems.

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

Institute for Advanced Study

On Minkowski's Monotonicity Problem in Convex Geometry

Delve into the geometric analysis of Minkowski's mixed volume monotonicity problem, exploring recent advances and connections to classical surface theory and convex geometry fundamentals.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

On Yuansi Chen's Work on the KLS Conjecture I

Explore the KLS conjecture in high-dimensional geometry, its implications for Bourgain's slicing problem, and recent progress using Eldan's Stochastic Localization technique.

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

Hausdorff Center for Mathematics

Separation Theorems in Signed Tropical Convexities

Explores separation theorems in signed tropical convexities, comparing TO and TC-convexities. Presents new results on hyperplane separation, characterizes segments and hemi-spaces, and proves equivalence for generic point collections.

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

Hausdorff Center for Mathematics

One More Proof of the Alexandrov-Fenchel Inequality

Explore a concise proof of the Alexandrov-Fenchel inequalities for mixed volumes of convex bodies, presented by Bo'az Klartag in collaboration with other mathematicians.

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

Hausdorff Center for Mathematics

Blaschke–Santaló Inequalities for Minkowski and Asplund Endomorphisms

Explores new isoperimetric inequalities for monotone Minkowski endomorphisms, extending to Asplund endomorphisms of log-concave functions, generalizing the Blaschke–Santaló inequality in convex geometric analysis.

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

Hausdorff Center for Mathematics

Ilya Molchanov - Random Sets Generated by Translates of a Convex Body

Explores K-hulls and K-strongly convex sets, analyzing facial structures and applying theory to random point samples. Discusses convergence of f-vectors and related probabilistic results.

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

Hausdorff Center for Mathematics

The Mysterious Extremals of the Alexandrov-Fenchel Inequality

Explore the Alexandrov-Fenchel inequality's extremal bodies, recent progress in characterizing them for convex polytopes, and insights into this fundamental problem in convex geometry.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

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
• On-Demand
• Free Video

International Mathematical Union

Keith Ball- The Probabilistic Character of Convex Domains

Explore the probabilistic nature of convex domains with mathematician Keith Ball, delving into geometric concepts and their applications in probability theory.

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

IMSA

Nonrational Toric Geometry III - Quasifolds, Foliations, Combinatorics and One-parameter Families

Explores nonrational toric geometry through quasifolds, foliations, and combinatorics, extending classical toric geometry to new contexts and examining one-parameter families of toric quasifolds.

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

Hausdorff Center for Mathematics

On Some Tight Convexity Inequalities for Symmetric Convex Sets

Explores tight convexity inequalities for symmetric convex sets, focusing on Gaussian measure, isoperimetric problems, and Dirichlet-Poincare inequality. Discusses progress using L2 methods and energy minimization.

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

BIMSA

Sharp Stability for the Brunn-Minkowski Inequality for Arbitrary Sets

Explore sharp stability in the Brunn-Minkowski inequality for arbitrary sets, delving into combinatorics and its connections with metric geometry and analysis.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video