Randomness is widely used in various areas of computer science, and many of the applications require uniform, uncorrelated bit. However, most sources of randomness in nature are defective and at best, only contain some amount of entropy. This leads to the area of randomness extraction, where an extractor is a deterministic procedure to produce pure random bits from a weak source. A central open problem (from the 80's) in this area is to extract from 2 independent weak sources (it is known that it is impossible to extract from just 1 weak source). In joint work with David Zuckerman, we resolve this problem. I will discuss the main ideas we use to solve this problem.
As a corollary of our 2-source extractor, we obtain exponential improvements in explicit constructions of Ramsey graphs, a central object in extremal combinatorics. This is in a line of work spanning the last 70 years in an attempt to meet Erdos' challenge of matching the probabilistic method.