Convex & Discrete Geometry Courses and Certifications

Fields Institute

An Invitation to Lattice Polytopes

Explore the fundamental concepts and applications of lattice polytopes in mathematics through expert insights from Christian Haase of Freie Universität Berlin.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• 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
• Self-Paced
• Free Video

Hausdorff Center for Mathematics

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

Hausdorff Center for Mathematics

Entropy, Isotropic Constant and Mahler's Conjecture

Explores connections between entropy, isotropic constant, and Mahler's conjecture in convex geometry. Discusses functional forms of Klartag's work and adaptations for log-concave functions.

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

Hausdorff Center for Mathematics

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

Hausdorff Center for Mathematics

The Aleksandrov Projection Theorem for Convex Lattice Polygons

Explore the discrete analogue of Aleksandrov's projection theorem for convex lattice polygons, examining counterexamples and their implications in Z^2.

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

Hausdorff Center for Mathematics

Pierre Calka- Close-Up on Random Convex Hulls

Explore random convex hulls, Hausdorff distance, and asymptotic expansions in this mathematical talk on geometric probability and stochastic geometry.

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

Institute for Advanced Study

Stability of Geometric Inequalities: Continuous and Discrete Perspectives

Explore geometric inequalities from continuous and discrete perspectives, focusing on stability in various mathematical contexts.

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

Institute for Advanced Study

Linear Stability of the Brunn-Minkowski Inequality

Delve into advanced mathematical concepts exploring the linear stability of Brunn-Minkowski inequality, examining volume control in convex geometry and its connections to additive combinatorics.

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

Centre de recherches mathématiques - CRM

On Liakopoulos's Dual Bollobás-Thomason Inequality

Explore advanced geometric inequalities and volume bounds for convex bodies through projections and intersections with coordinate hyperplanes and subspaces.

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

Hausdorff Center for Mathematics

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

Hausdorff Center for Mathematics

Some Problems About Centroids of Convex Bodies

Explore recent advancements in understanding centers of mass for convex bodies, delving into mathematical concepts and their implications.

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