Completed
Energy minimizer's obviously depend on f
Class Central Classrooms beta
YouTube videos curated by Class Central.
Classroom Contents
Introduction to Sphere Packing Problems by Abhinav Kumar
Automatically move to the next video in the Classroom when playback concludes
- 1 Introduction Sphere Packing problem
- 2 What is this your packing problem?
- 3 Collection of spheres
- 4 What is the density of these spheres?
- 5 Some answers which are known only in some small dimensions
- 6 Stack layers of the hexagonal lattice
- 7 Hexagonal planar packing
- 8 Why is this the best?
- 9 These are the densest proof by hales & collaborators
- 10 What we can guess in some higher dimensions?
- 11 Low dimensional lattices
- 12 What are all the densest packing's in low dimension and fiber in construction?
- 13 Modular lattices
- 14 Infinity many possibilities and they are obtained by suitable coloring of a packing
- 15 For along time it was suspected that E8 lattice packing was the unique densest
- 16 All kinds of strange things happen
- 17 First dimension the densest known packing is a non lattice & its consists of 40 trsanslates
- 18 What about higher dimensions?
- 19 What happens between ten and twenty four?
- 20 Upper and easy lower bound
- 21 Lower bound
- 22 Lattices
- 23 What is the densest lattice in dimensions?
- 24 Flow conjecture in high dimensions
- 25 Asymptotics
- 26 What the best lattices should look like in very high dimensions?
- 27 Spherical codes
- 28 Kissing number problem
- 29 Energy Minimization
- 30 Energy minimizer's obviously depend on f
- 31 Open problem
