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Title:
On Zaremba's Conjecture on Continued Fractions

Speaker:
Jean Bourgain

Abstract:
Zaremba's 1971 conjecture predicts that every integer appears as the denominator of a finite continued fraction whose partial quotients are bounded by an absolute constant. We confirm this conjecture for a set of density one.

Link:
https://www.ias.edu/video/analysis/bourgain