Mathematics Colloquia and Seminars

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Although only rational numbers can be observed in experiments, physicists, wanting the tools of analysis, have traditionally built models which use the whole real number field. The real numbers are one of many completions of the rationals. Ostrowski showed that any such completion is equivalent to either the real numbers or the p-adic numbers for some prime p. The field of adels puts all of these completions on equal footing and the strong approximation theorem allows one to express functions of real variables with some discrete symmetries as functions of adels. Examples from physics of this "adelization" process will be given.