# Jean Bourgain

## A spectral gap in $\mathrm{SL}^2(\mathbb R)$ and applications: expansion, Furstenberg measures and the Anderson-Bernoulli model

Jean Bourgain
IBM von Neumann Professor, School of Mathematics
November 30, 2016

## On Zaremba's Conjecture on Continued Fractions

Jean Bourgain
Institute for Advanced Study
February 14, 2012
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.

## Expansion in Linear Groups and Applications

Jean Bourgain, Professor, School of Mathematics
Institute for Advanced Study
September 24, 2010

This lecture was part of the Institute for Advanced Study’s celebration of its eightieth anniversary, and took place during the events related to the Schools and Mathematics and Natural Sciences.

## PMSP - Expansion in Lie groups and applications

Jean Bourgain
Institute for Advanced Study
June 16, 2010

## Pseudorandomness - Exponential sums, equidistribution and pseudo-randomness

Jean Bourgain
Institute for Advanced Study
December 3, 2008