Yin Tat Lee, Aaron Sidford. Path Finding Methods for Linear Programming: Solving Linear Programs in Õ(vrank) Iterations and Faster Algorithms for Maximum Flow. FOCS 2014. First theoretic improvement on the running time of linear programming since 1986. Best Paper and Best Student Paper in FOCS 2014. Selected as a notable article in computing in 2014 by Computing Reviews. (Part 1)(Part 2)
Michael B. Cohen, Yin Tat Lee, Gary L. Miller, Jakub W. Pachocki, Aaron Sidford. Geometric Median in Nearly Linear Time. STOC 2016. First example problems that interior point method provably takes nearly linear time.
Michael B. Cohen, Yin Tat Lee, Cameron Musco, Christopher Musco, Richard Peng, Aaron Sidford. Uniform Sampling for Matrix Approximation. ITCS 2015. Solving a system of a tall matrix is as easy as a square matrix.