Linus Hamilton

In recent years there has been significant effort to adapt the key tools and ideas in convex optimization to the Riemannian setting. One key challenge has remained: Is there a Nesterov-like accelerated gradient method for geodesically…

The Paulsen problem is a basic problem in operator theory that was resolved in a recent tour-de-force work of Kwok, Lau, Lee and Ramachandran. In particular, they showed that every $\epsilon$-nearly equal norm Parseval frame in $d$…

We analyze the computational complexity of the many types of pencil-and-paper-style puzzles featured in the 2016 puzzle video game The Witness. In all puzzles, the goal is to draw a simple path in a rectangular grid graph from a start…

Markov random fields area popular model for high-dimensional probability distributions. Over the years, many mathematical, statistical and algorithmic problems on them have been studied. Until recently, the only known algorithms for…

Braid is a 2008 puzzle game centered around the ability to reverse time. We show that Braid can simulate an arbitrary computation. Our construction makes no use of Braid's unique time mechanics, and therefore may apply to many other video…

The Internet has emerged as perhaps the most important network in modern computing, but rather miraculously, it was created through the individual actions of a multitude of agents rather than by a central planning authority. This motivates…