## Research

It’s math; in fact, it is applied math! Applied to what? Read on…

Multigrid research numerically solves linear systems such as **A**x = **b**. Simple enough! But, this linear system may have thousands or even millions of rows! A key to quickly solving such systems in multigrid is uncovering smooth components of the error. To the left, we have algebraically smooth, although not geometrically smooth, error which could be used to construct an efficient method. Highlights include work with Lawrence Livermore and Los Alamos National Laboratories where multigrid is commonly used on some of the world’s fastest supercomputers.

We all benefit from ranking of webpages with search engines. Our work includes ranking webpages, including work on ranking Twitter accounts. Who would be the most important? What model do you use? We have also ranked sports teams which includes the creation of mathematically-generated brackets for March Madness. Ranking can be applied to a variety of contexts — for instance, movies. Keep in mind, it isn’t enough to create a top 10 list…it has to have meaning which stems from a strong underlying mathematical model.

Clustering mines through large datasets looking for patterns that can lead to insight. To the left we see a small network of movies. This grew from clustering movies from the Netflix Prize data. We used user ratings to cluster movies and define mathematical genres. Have a favorite movie? We may have a recommendation.