Spheres | Discrete geometry | Packing problems
In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space. The spheres considered are usually all of identical size, and the space is usually three-dimensional Euclidean space. However, sphere packing problems can be generalised to consider unequal spheres, spaces of other dimensions (where the problem becomes circle packing in two dimensions, or hypersphere packing in higher dimensions) or to non-Euclidean spaces such as hyperbolic space. A typical sphere packing problem is to find an arrangement in which the spheres fill as much of the space as possible. The proportion of space filled by the spheres is called the packing density of the arrangement. As the local density of a packing in an infinite space can vary depending on the volume over which it is measured, the problem is usually to maximise the average or asymptotic density, measured over a large enough volume. For equal spheres in three dimensions, the densest packing uses approximately 74% of the volume. A random packing of equal spheres generally has a density around 63.5%. (Wikipedia).
Introduction Sphere Packing problems by Abhinav Kumar
DISCUSSION MEETING SPHERE PACKING ORGANIZERS: Mahesh Kakde and E.K. Narayanan DATE: 31 October 2019 to 06 November 2019 VENUE: Madhava Lecture Hall, ICTS Bangalore Sphere packing is a centuries-old problem in geometry, with many connections to other branches of mathematics (number the
From playlist Sphere Packing - 2019
Inverse problem by Abhinav Kumar
DISCUSSION MEETING SPHERE PACKING ORGANIZERS: Mahesh Kakde and E.K. Narayanan DATE: 31 October 2019 to 06 November 2019 VENUE: Madhava Lecture Hall, ICTS Bangalore Sphere packing is a centuries-old problem in geometry, with many connections to other branches of mathematics (number the
From playlist Sphere Packing - 2019
Discussion Meeting Sphere Packing ORGANIZERS: Mahesh Kakde and E.K. Narayanan DATE: 31 October 2019 to 06 November 2019 VENUE: Madhava Lecture Hall, ICTS Bangalore Sphere packing is a centuries-old problem in geometry, with many connections to other branches of mathematics (number the
From playlist Sphere Packing - 2019
Quadratic forms and Hermite constant, reduction theory by Radhika Ganapathy
Discussion Meeting Sphere Packing ORGANIZERS: Mahesh Kakde and E.K. Narayanan DATE: 31 October 2019 to 06 November 2019 VENUE: Madhava Lecture Hall, ICTS Bangalore Sphere packing is a centuries-old problem in geometry, with many connections to other branches of mathematics (number the
From playlist Sphere Packing - 2019
Semidefinte programming bounds by Abhinav Kumar
DISCUSSION MEETING SPHERE PACKING ORGANIZERS: Mahesh Kakde and E.K. Narayanan DATE: 31 October 2019 to 06 November 2019 VENUE: Madhava Lecture Hall, ICTS Bangalore Sphere packing is a centuries-old problem in geometry, with many connections to other branches of mathematics (number the
From playlist Sphere Packing - 2019
Positive definite kernels on spheres by E K Narayanan
DISCUSSION MEETING SPHERE PACKING ORGANIZERS: Mahesh Kakde and E.K. Narayanan DATE: 31 October 2019 to 06 November 2019 VENUE: Madhava Lecture Hall, ICTS Bangalore Sphere packing is a centuries-old problem in geometry, with many connections to other branches of mathematics (number the
From playlist Sphere Packing - 2019
Universal optimality proof by Abhinav Kumar
DISCUSSION MEETING SPHERE PACKING ORGANIZERS: Mahesh Kakde and E.K. Narayanan DATE: 31 October 2019 to 06 November 2019 VENUE: Madhava Lecture Hall, ICTS Bangalore Sphere packing is a centuries-old problem in geometry, with many connections to other branches of mathematics (number the
From playlist Sphere Packing - 2019
From playlist Drawing a sphere
Energy minimization by Abhinav Kumar
DISCUSSION MEETING SPHERE PACKING ORGANIZERS: Mahesh Kakde and E.K. Narayanan DATE: 31 October 2019 to 06 November 2019 VENUE: Madhava Lecture Hall, ICTS Bangalore Sphere packing is a centuries-old problem in geometry, with many connections to other branches of mathematics (number the
From playlist Sphere Packing - 2019
The Best Way to Pack Spheres - Numberphile
Featuring James Grime... Check out Brilliant (and get 20% off their premium service): https://brilliant.org/numberphile (sponsor) More links & stuff in full description below ↓↓↓ Sphere trilogy: http://bit.ly/Sphere_Trilogy Strange Spheres in Higher Dimensions: https://youtu.be/mceaM2_zQ
From playlist Sphere Trilogy on Numberphile
Diophantine analysis in thin orbits - Alex Kontorovich
Special Seminar Topic: Diophantine analysis in thin orbits Speaker: Alex Kontorovich Affiliation: Rutgers University; von Neumann Fellow, School of Mathematics Date: December 8, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Sphere packings in 8 dimensions (after Maryna Viazovska)
The is a math talk about the best possible sphere packing in 8 dimensions. It was an open problem for many years to show that the best 8-dimensional sphere packing is given by the E8 lattice. We describe the solution to this found by Maryna Viazovska, building on work of Henry Cohn and Noa
From playlist Math talks
Disentangling the role of structure and friction in shear jamming by Srikanth Sastry
Discussion Meeting: Nonlinear Physics of Disordered Systems: From Amorphous Solids to Complex Flows URL: http://www.icts.res.in/discussion_meeting/NPDS2015/ Dates: Monday 06 Apr, 2015 - Wednesday 08 Apr, 2015 Description: In recent years significant progress has been made in the physics
From playlist Discussion Meeting: Nonlinear Physics of Disordered Systems: From Amorphous Solids to Complex Flows
A Breakthrough in Higher Dimensional Spheres | Infinite Series | PBS Digital Studios
Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi How do you stack hundred-dimensional oranges? Learn about recent breakthroughs in our understanding of hyperspheres in the first episode of Infinite Series, a show tha
From playlist Higher Dimensions
Geometry and arithmetic of sphere packings - Alex Kontorovich
Members' Seminar Topic: Geometry and arithmetic of sphere packings Speaker: A nearly optimal lower bound on the approximate degree of AC00 Speaker:Alex Kontorovich Affiliation: Rutgers University Date: October 23, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
History of science 7: Did Witt discover the Leech lattice?
In about 1970 the German mathematician Witt claimed to have discovered the Leech lattice many years before Leech. This video explains what the Leech lattice is and examines the evidence for Witt's claim. Lieven Lebruyn discussed this question on his blog: http://www.neverendingbooks.org/w
From playlist History of science
This is an informal talk on sporadic groups given to the Archimedeans (the Cambridge undergraduate mathematical society). It discusses the classification of finite simple groups and some of the sporadic groups, and finishes by briefly describing monstrous moonshine. For other Archimedeans
From playlist Math talks
Florian Frick (6/4/21): Rips complexes, projective codes, and zeros of odd maps
We will discuss a relation between the topology of Rips complexes (or their metric versions), the size of codes in projective spaces, and structural results for the zero set of odd maps from spheres to Euclidean space. On the one hand, this provides a new topological approach to problems i
From playlist Vietoris-Rips Seminar
http://demonstrations.wolfram.com/CubicClosePackingCube/ The Wolfram Demonstration Project contains thousands of free interactive visualizations with new entries added daily. Close-packed layers of spheres can be stacked to form a cubic close packing by shifting every second layer. M
From playlist Wolfram Demonstrations Project