Sphere Packing Courses and Certifications

International Mathematical Union

Oded Regev: The Reverse Minkowski Theorem

Explore the Reverse Minkowski Theorem, its applications, and open questions in lattice theory with mathematician Oded Regev in this insightful mathematical lecture.

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

International Centre for Theoretical Sciences

Modular Forms by Mahesh Kakde

Comprehensive exploration of modular forms, covering definitions, properties, and applications. Delves into Eisenstein series, theta functions, and related mathematical concepts for advanced learners in number theory.

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

International Centre for Theoretical Sciences

Introduction to Sphere Packing Problems by Abhinav Kumar

Explore sphere packing in geometry, covering its history, applications, and recent advances. Learn about lattices, codes, bounds, and energy minimization in various dimensions.

• YouTube
• 1 hour 39 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Quadratic Forms and Hermite Constant, Reduction Theory by Radhika Ganapathy

Explores techniques for computing densest lattice packings, including quadratic forms, Hermite constants, and reduction theory. Covers perfect forms, eutactic lattices, and Voronoi's algorithm for listing perfect forms.

• YouTube
• 1 hour 24 minutes
• On-Demand
• Free Video

Fields Institute

Maximally Dense Sphere Packings

Explore optimal arrangements of disks in 2D and higher dimensions, focusing on recent findings for multiple disk sizes. Survey of results accessible to a broad audience.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Simons Institute

Back to the Future: The Evolution of Coding Theory Through Reed Muller Codes

Explore the evolution of coding theory through Reed Muller codes, from sphere packing to iterative algorithms and quantum computing applications.

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

Institut des Hautes Etudes Scientifiques (IHES)

Random Lattices as Sphere Packings

Explore lattice-sum functions and their applications in sphere packing density, including Siegel's mean value theorem and recent advancements in optimal packing bounds.

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

Isaac Newton Institute for Mathematical Sciences

Thomson's 5 Point Problem and Power-Law Potentials - Rothschild Lecture

Explore Thomson's 5 point problem and its phase transition constant through rigorous computer-assisted proof. Gain insights into electrostatic potential minimization and power-law potentials on spheres.

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

PoreLab

Frustrated Bearings: Exploring Minimum Energy Dissipation in Sphere Systems

Explore the fascinating world of frustrated bearings, their unique properties, and applications in physics and engineering. Discover how these systems exhibit novel states and unexpected behaviors in 2D and 3D.

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

Centre de recherches mathématiques - CRM

Linear Programming Bounds for Hyperbolic Surfaces

Explore new upper bounds on geometric and spectral invariants of closed hyperbolic surfaces using the Selberg trace formula and linear programming techniques.

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