# On Zaremba's Conjecture

## On Zaremba's Conjecture - Alex Kontorovich

Alex Kontorovich
Stony Brook University
April 22, 2011

Inspired by the theory of good lattice points in numerical integration, Zaremba conjectured in 1972 that for every denominator q, there is some coprime numerator p, such that the continued fraction expansion of p/q has uniformly bounded quotients. We will present recent progress on this problem, joint with Jean Bourgain.