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Das Problem der Kugelpackung

Snapshots of modern mathematics from Oberwolfach

Das Problem der Kugelpackung

Wie würdest du Tennisbälle oder Orangen stapeln? Oder allgemeiner formuliert: Wie dicht lassen sich identische 3-dimensionale Objekte überschneidungsfrei anordnen? Das Problem, welches auch Anwendungen in der digitalen Kommunikation hat, hört sich einfach an, ist jedoch für Kugeln in höheren Dimensionen noch immer ungelöst. Sogar die Berechnung guter Näherungslösungen ist für die meisten Di- mensionen schwierig. 

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Mathematical subjects

Algebra and Number Theory
Discrete Mathematics and Foundations
Geometry and Topology

Connections to other fields

Chemistry and Earth Science
Computer Science
Physics
Reflections on Mathematics

Author(s)

Maria Dostert, Stefan Krupp, Jan Hendrick Rolfes

License

DOI (Digital Object Identifier)

10.14760/SNAP-2016-004-EN

Download PDF

2016-004-dostert-rolfes-krupp.pdf

PDF

snapshots: overview

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      The periodic tables of algebraic geometry
      Jason J. Bramburger
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      Benjamin Dozier
      Closed geodesics on surfaces
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      Characterizations of intrinsic volumes on convex bodies and convex functions
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      A tale of three curves
      Michael Baake, Uwe Grimm, Robert V. Moody
      What is Pattern?
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      Biological Shape Analysis with Geometric Statistics and Learning
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      Representations and degenerations
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      Solving inverse problems with Bayes’ theorem
      Herbert Gangl
      Jewellery from tessellations of hyperbolic space
      Chr istina Frederick, Yunan Yang
      Seeing through rock with help from optimal transport
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      Searching for the Monster in the Trees
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      The Robinson–Schensted algorithm
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      Emergence in biology and social sciences
      Jason D. Lotay
      Lagrangian mean curvature flow
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      Finite geometries: pure mathematics close to applications
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      Describing distance: from the plane to spectral triples
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      Quantum symmetry
      Fadoua Balabdaoui, Yulia Kulagina
      The Enigma behind the Good–Turing formula
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      Reflections on hyperbolic space
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      Quantum symmetry
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      Determinacy versus indeterminacy
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      Vertex-to-Self Trajectories on the Platonic Solids
      Gianluca Finocchio
      Random matrix theory: Dyson Brownian motion
      Holger Kammeyer, Roman Sauer
      From Betti numbers to l2-Betti numbers
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      Is it possible to predict the far future before the near future is known accurately?
      Jan-Bernhard Kordaß
      The Interaction of Curvature and Topology
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      The Mathematics of Fluids and Solids
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      A surprising connection between quantum mechanics and shallow water waves
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      Formation Control and Rigidity Theory
      Ana Khukhro
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      Mixed-dimensional models for real-world applications
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      Configuration spaces and braid groups
      Tereza Klimošová
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      On Logic, Choices and Games
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      Nonlinear Acoustics
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      Random permutations
      Hugo Duminil-Copin
      Counting self-avoiding walks on the hexagonal lattice
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      Jonathan Rosenberg, David Wraith
      Positive Scalar Curvature and Applications
      Hector Pasten
      Diophantine equations and why they are hard
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      Estimating the volume of a convex body
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      Mixed volumes and mixed integrals
      Filippo Santambrogio
      A short story on optimal transport and its many applications
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      Number theory in quantum computing
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      Data assimilation: mathematics for merging models and data
      Claus Hertling
      Geometry behind one of the Painlevé III differential equations
      Antonio Lerario
      The codimension
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      The mathematics of aquatic locomotion
      Erwan Brugallé, Ilia Itenberg, Kristin Shaw, Oleg Viro
      Tropical geometry
      Alex Barnett
      Fast Solvers for Highly Oscillatory Problems
      Greg Lupton, John Oprea, José Gabriel Carrasquel Vera
      Topological Complexity, Robotics and Social Choice
      Thomas Sauer
      Prony’s method: an old trick for new problems
      Colva M. Roney-Dougal
      Computing with symmetries
      Piotr Sułkowski
      Topological recursion
      Anna Seigal
      The Algebraic Statistics of an Oberwolfach Workshop
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      Solving quadratic equations in many variables
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      Mathematics plays a key role in scientific computing
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      Spaces of Riemannian metrics
      Shaula Fiorelli Vilmart, Gilles Vilmart
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      Justin Solomon
      Computational Optimal Transport
      Justyna Szpond
      A few shades of interpolation
      George Hagedorn, Caroline Lasser
      Molecular quantum dynamics
      Marco Radeschi
      Closed geodesics on surfaces and Riemannian manifolds
      Christian Engwer, Markus Knappitsch
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      Michael Baake, David Damanik, Uwe Grimm
      Aperiodic Order and Spectral Properties
      Lukas Pottmeyer
      News on quadratic polynomials
      Felix Günther
      Winkeltreue zahlt sich aus
      Jacob Bedrossian
      Towards a Mathematical Theory of Turbulence in Fluids
      Laurent Bartholdi
      Profinite groups
      Dietmar Gallistl
      The adaptive finite element method
      Steven Klee
      Footballs and donuts in four dimensions
      Nikolai Nowaczyk
      The Willmore Conjecture
      Lior Bary-Soroker
      Prime Tuples in Function Fields
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      Polyhedra and commensurability
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      High performance computing on smartphones
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      Symmetry and characters of finite groups
      Maria Dostert, Stefan Krupp, Jan Hendrick Rolfes
      Das Problem der Kugelpackung
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      On the containment problem
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      Random sampling of domino and lozenge tilings
      Magnus Egerstedt
      Swarming robots
      Ulrich Krähmer
      From computer algorithms to quantum field theory: an introduction to operads
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      Domino tilings of the Aztec Diamond
      Sebastian Funk
      The mystery of sleeping sickness – why does it keep waking up?
      Antti Knowles
      Quantum diffusion
      Amanda Swan, Albert Murtha
      Modelling the spread of brain tumours
      J. Marron
      Visual Analysis of Spanish Male Mortality
      Christopher Sangwin
      Curriculum development in university mathematics: where mathematicians and education collide
      Jürg Kramer, Anna-Maria Pippich
      Special values of zeta functions and areas of triangles
      Victoria Powers
      How to choose a winner : the mathematics of social choice
      Valentina Kiritchenko, Evgeny Smirnov, Vladlen Timorin
      Ideas of Newton-Okounkov bodies
      Ben Schweizer
      Darcy’s law and groundwater flow modelling
      Raluca Eftimie
      Modelling communication and movement: from cells to animals and humans
      Tom Solomon
      Chaos and chaotic fluid mixing
      Thorsten Holm
      Friezes and tilings
      George Willis
      Zero-dimensional symmetry
      Christine Breiner
      Minimizing energy
      Diana Davis
      Billiards and flat surfaces
      Peter Benner, Hermann Mena, René Schneider
      Drugs, herbicides, and numerical simulation
      Gregory Knese
      Operator theory and the singular value decomposition
      Alain Valette
      The Kadison-Singer problem
      Ragnar-Olaf Buchweitz, Eleonore Faber
      Swallowtail on the shore
      Howell Tong
      Statistics and dynamical phenomena
      Brian Harbourne, Thomas Szemberg
      Arrangements of lines
      Bruce Reznick
      What does ">" really mean?
      Harald Helfgott
      The ternary Goldbach Problem
      Wolfgang Lerche
      Matrixfaktorisierungen
      John E. McCarthy
      Dirichlet Series

      Mathematical subjects

      Algebra and Number Theory
      Analysis
      Didactics and Education
      Discrete Mathematics and Foundations
      Geometry and Topology
      Numerics and Scientific Computing
      Probability Theory and Statistics

      Connections to other fields

      Chemistry and Earth Science
      Computer Science
      Engineering and Technology
      Finance
      Humanities and Social Sciences
      Life Science
      Physics
      Reflections on Mathematics

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