Euclidean solid geometry

Finite sphere packing

In mathematics, the theory of finite sphere packing concerns the question of how a finite number of equally-sized spheres can be most efficiently packed. The question of packing finitely many spheres has only been investigated in detail in recent decades, with much of the groundwork being laid by László Fejes Tóth. The similar problem for infinitely many spheres has a longer history of investigation, from which the Kepler conjecture is most well-known. Atoms in crystal structures can be simplistically viewed as closely-packed spheres and treated as infinite sphere packings thanks to their large number. Sphere packing problems are distinguished between packings in given containers and free packings. This article primarily discusses free packings. (Wikipedia).

Finite sphere packing
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Combinatorics and Geometry to Arithmetic of Circle Packings - Nakamura

Speaker: Kei Nakamura (Rutgers) Title: Combinatorics and Geometry to Arithmetic of Circle Packings Abstract: The Koebe-Andreev-Thurston/Schramm theorem assigns a conformally rigid fi-nite circle packing to a convex polyhedron, and then successive inversions yield a conformally rigid infin

From playlist Mathematics

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Sharp sphere packings – Maryna Viazovska – ICM2018

Number Theory | Combinatorics Invited Lecture 3.1 | 13.1 Sharp sphere packings Maryna Viazovska Abstract: In this talk we will speak about recent progress on the sphere packing problem. The packing problem can be formulated for a wide class of metric spaces equipped with a measure. An in

From playlist Number Theory

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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

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Upper 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

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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

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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

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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

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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

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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

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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

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Sporadic groups

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

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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

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Jessica Purcell - Lecture 2 - Fully augmented links and circle packings

Jessica Purcell, Monash University Title: Fully augmented links and circle packings Fully augmented links form a family of hyperbolic links that are a playground for hands-on hyperbolic geometry. In the first part of the talk, I’ll define the links and show how to determine their hyperboli

From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022

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Recent Progresses in The Mean-Field Approach to the Jamming Transition by Francesco Zamponi

DISCUSSION MEETING : CELEBRATING THE SCIENCE OF GIORGIO PARISI (ONLINE) ORGANIZERS : Chandan Dasgupta (ICTS-TIFR, India), Abhishek Dhar (ICTS-TIFR, India), Smarajit Karmakar (TIFR-Hyderabad, India) and Samriddhi Sankar Ray (ICTS-TIFR, India) DATE : 15 December 2021 to 17 December 2021 VE

From playlist Celebrating the Science of Giorgio Parisi (ONLINE)

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Thin Groups and Applications - Alex Kontorovich

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From playlist Analysis and Beyond

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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

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Coverings of the Circle

A covering of a topological space X is a topological space Y together with a continuous surjective map from X to Y that is locally bi-continuos. The infinite spiral is for example a covering of the circle. Notice how every path on the circle can be lifted to the spiral. If a coveri

From playlist Algebraic Topology

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High density phases of hard-core lattice particle systems - Ian Jauslin

Members' Seminar Topic: High density phases of hard-core lattice particle systems Speaker: Ian Jauslin Affiliation: Member, School of Mathematics Date: October 30, 2017 For more videos, please visit http://video.ias.edu

From playlist Mathematics

Related pages

Minkowski addition | Graph (discrete mathematics) | Hermann Minkowski | Geometry of numbers | Convex hull | Packing density | Convex geometry | Brunn–Minkowski theorem | Vertex (graph theory) | László Fejes Tóth | Mixed volume | Claude Ambrose Rogers | Cylinder | Sphere | Kepler conjecture | Tetrahedron | Convex set | Close-packing of equal spheres