Universality for mathematical and physical systems

Research output: Contribution to conferencePaper

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)
Pages125-152
Number of pages28
StatePublished - Dec 1 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

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Keywords

  • Random matrices
  • Riemann-hilbert problems
  • Universality

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Deift, P. (2006). Universality for mathematical and physical systems. 125-152. Paper presented at 25th International Congress of Mathematicians, ICM 2006, Madrid, Spain.