Symmetry, invariance and the structure of matter

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations


We present a mathematical view of the structure of matter based on the invariance of the classical equations of physics.

Original languageEnglish (US)
Title of host publicationInvited Lectures
EditorsBoyan Sirakov, Paulo Ney de Souza, Marcelo Viana
PublisherWorld Scientific Publishing Co. Pte Ltd
Number of pages28
ISBN (Electronic)9789813272934
StatePublished - 2018
Event2018 International Congress of Mathematicians, ICM 2018 - Rio de Janeiro, Brazil
Duration: Aug 1 2018Aug 9 2018

Publication series

NameProceedings of the International Congress of Mathematicians, ICM 2018


Conference2018 International Congress of Mathematicians, ICM 2018
CityRio de Janeiro

Bibliographical note

Funding Information:
This work was supported by AFOSR (FA9550-15-1-0207), NSF (DMREF-1629026), ONR (N00014-14-1-0714), and the MURI program (FA9550-12-1-0458, FA9550-16-1-0566). MSC2010: primary 82-02; secondary 20H15, 35Q60, 51F25, 70H33, 78A45. Keywords: Atomic structure, symmetry, objective structures, isometry groups, molecular dynamics, invariant manifold, Boltzmann equation, homoenergetic solutions, Maxwell’s equations, non-equilibrium statistical mechanics, X-ray methods.

Publisher Copyright:
© ICM 2018.All rights reserved.


  • Atomic structure
  • Boltzmann equation
  • Homoenergetic solutions
  • Invariant manifold
  • Isometry groups
  • Maxwell’s equations
  • Molecular dynamics
  • Non-equilibrium statistical mechanics
  • Objective structures
  • Symmetry
  • X-ray methods


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