In 1960 Rudolph Kalman published what is arguably the first paper to develop a systematic, principled approach to the use of data to improve the predictive capability of mathematical models. As our ability to gather data grows at an enormous rate, the importance of this work continues to grow too. The lecture will describe Kalman's paper and how it lead to other algorithms, including ensemble Kalman filtering. These methods have revolutionized applications such as navigation, weather prediction, oceanography, oil recovery and medical imaging; and they shows promise to impact other areas such as machine learning. Various applications will be highlighted in the talk.

Algorithms will be introduced through a simple iterative optimization framework. Despite their widespread use in applications, ensemble Kalman methods have attracted limited analysis. The talk will conclude by explaining a framework for their analysis, based on mean-field interacting particle systems, and recent theoretical results stemming from this framework.