Universality for mathematical and physical systems

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

Abstract

All physical systems in equilibrium obey the laws of thermodynamics. In other words, whatever the precise nature of the interaction between the atoms and molecules at the microscopic level, at the macroscopic level, physical systems exhibit universal behavior in the sense that they are all governed by the same laws and formulae of thermodynamics. In this paper we describe some recent history of universality ideas in physics starting with Wigner's model for the scattering of neutrons off large nuclei and show how these ideas have led mathematicians to investigate universal behavior for a variety of mathematical systems. This is true not only for systems which have a physical origin, but also for systems which arise in a purely mathematical context such as the Riemann hypothesis, and a version of the card game solitaire called patience sorting.

Original languageEnglish (US)
Title of host publicationInternational Congress of Mathematicians, ICM 2006
Pages125-152
Number of pages28
Volume1
StatePublished - 2006
Event25th International Congress of Mathematicians, ICM 2006 - Madrid, Spain
Duration: Aug 22 2006Aug 30 2006

Other

Other25th International Congress of Mathematicians, ICM 2006
CountrySpain
CityMadrid
Period8/22/068/30/06

Fingerprint

Universality
Thermodynamics
Solitaire
Riemann hypothesis
Neutron
Sorting
Nucleus
Physics
Molecules
Scattering
Game
Interaction
Model

Keywords

  • Random matrices
  • Riemann-hilbert problems
  • Universality

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Deift, P. (2006). Universality for mathematical and physical systems. In International Congress of Mathematicians, ICM 2006 (Vol. 1, pp. 125-152)

Universality for mathematical and physical systems. / Deift, Percy.

International Congress of Mathematicians, ICM 2006. Vol. 1 2006. p. 125-152.

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

Deift, P 2006, Universality for mathematical and physical systems. in International Congress of Mathematicians, ICM 2006. vol. 1, pp. 125-152, 25th International Congress of Mathematicians, ICM 2006, Madrid, Spain, 8/22/06.
Deift P. Universality for mathematical and physical systems. In International Congress of Mathematicians, ICM 2006. Vol. 1. 2006. p. 125-152
Deift, Percy. / Universality for mathematical and physical systems. International Congress of Mathematicians, ICM 2006. Vol. 1 2006. pp. 125-152
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