Los puntos de Fekete y el s

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Los puntos de Fekete y el séptimo problema de
Smale

• Grupo VARIDIS Enrique Bendito, Ángeles Carmona,
• Andrés Marcos Encinas, Jose Manuel Gesto, Agustín
  Medina.
• Deptartamento de Matemática Aplicada III

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Outline

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Part I Introduction to the Fekete problem and
to the Forces Method
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The Fekete problem
The search of the regularity
Stone models of the five Platonic polyhedra. They
date from about 2000BC and are kept in the
Ashmolean Museum in Oxford (figure extracted from
a work by Atiyah and Sutcliffe).
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The Fekete problem
Best-packing problem Maximize the minimum
distance between points constraints.
(Nurmela)
The solutions of this problem define lattices
that exhibite a high degree of regularity
(many equilateral triangles).
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The Fekete problem
I. Newton (1643-1727)
N. Copernicus (1473-1543)
G. Galilei (1564-1642)
J. Kepler (1571-1630)
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The Fekete problem
Ch.A. de Coulomb (1736-1806)
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The Fekete problem
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The Fekete problem
J.J. Thomson (1856-1940)
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The Fekete problem
A. Einstein (1879-1955)
M.K. Planck (1858-1947)
N. Bohr (1885-1962)
E. Schrödinger (1887-1961)
W. Heisenberg (1901-1979)
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The Fekete problem
Molecular Mechanics, Electrostatics,
Crystallography, structures of viruses, proteins,
bacteri, multi-electron bubbles, microclusters of
rare gases
(AtiyahSutcliffe)
(Bowick et al.)
Van der Waals interaction Lennard-Jones energy
J.D. van der Waals (1837-1923)
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The Fekete problem
M. Fekete (1886-1957)
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The Fekete problem
G. Polya (1887-1985)
G. Szegö (1895-1985)
O. Frostman (1907-1977)
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The Fekete problem
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The Fekete problem
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The Fekete problem
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Smales 7th problem
S. Smale (1930- )
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Smales 7th problem
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Smales 7th problem
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Smales 7th problem
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Smales 7th problem
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Smales 7th problem
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Smales 7th problem
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State of the art
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State of the art
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State of the art
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State of the art
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State of the art
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State of the art
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The Forces Method
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The Forces Method
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Numerical experiments
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Numerical experiments
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Numerical experiments
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Numerical experiments
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Numerical experiments
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Numerical experiments
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The cost of a local minimum
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The cost of a local minimum
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The cost of a local minimum
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The energy
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Large scale experiments
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Large scale experiments
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Large scale experiments
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The FinisTerrae challenge
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The FinisTerrae challenge
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The FinisTerrae challenge
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The FinisTerrae challenge
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The FinisTerrae challenge
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