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• W2950113968 abstract "It has been remarked that a fair measure of the impact of Atle Selberg's work is the number of mathematical terms which bear his name. One of these is the Selberg integral, an n-dimensional generalization of the Euler beta integral. We trace its sudden rise to prominence, initiated by a question to Selberg from Enrico Bombieri, more than thirty years after publication. In quick succession the Selberg integral was used to prove an outstanding conjecture in random matrix theory, and cases of the Macdonald conjectures. It further initiated the study of q-analogues, which in turn enriched the Macdonald conjectures. We review these developments and proceed to exhibit the sustained prominence of the Selberg integral, evidenced by its central role in random matrix theory, Calogero-Sutherland quantum many body systems, Knizhnik-Zamolodchikov equations, and multivariable orthogonal polynomial theory." @default.
• W2950113968 created "2019-06-27" @default.
• W2950113968 creator A5019351501 @default.
• W2950113968 creator A5028883197 @default.
• W2950113968 date "2007-10-22" @default.
• W2950113968 modified "2023-09-27" @default.
• W2950113968 title "The importance of the Selberg integral" @default.
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• W2950113968 hasPublicationYear "2007" @default.
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