Dr. Xavier Tricoche

"Visualizing the Topology of Tensor Fields"

In this presentation I will describe and discuss the topological approach to tensor field visualization.

This technique developed over the last decade has proved successful in permitting an efficient reduction of the rich amount of information enclosed by tensor quantities while allowing for insightful and accurate analysis of complex data sets. Its mathematical foundations lead back to both the qualitative theory of dynamical systems and differential geometry.

The essential notions of tensor topology will be introduced. In particular, I will explain the fundamental relationship between vector and tensor topology which is key for visualization purposes. The basic technique will be described along with improvements designed to meet the requirements of practical applications, including time-dependency and intricacy of typical data sets.