January 24th (Fri)

Place 342, Building No.3, Grad. Sch. of Eng. (工学部 3 号館 342)
contact Center for Computational Science

Time 10:40-
Konstantin Mischaikow
Rutgers University
Analysis of Complex Spatio-Temporal Patterns via Computational Algebraic Topology
Patterns produced by nonlinear systems and observed either through experiment or numerical simulation can be thought of as projections from an infinite dimensional phase space onto a finite (even discrete) observation space. However, since this observation space is still typically very high dimensional, it is often necessary to further simplify the data. Observe that the projection of interest often takes the form a scalar function, i.e. pressure, temperature, magnitude of forces or stress. The relatively young field of topological data analysis is providing new tools for performing the desired simplification of the data. The focus of this talk is one such tool called persistent homology. We will discuss the theory behind the tool, new algorithms that allow for its efficient computation even for large data sets, and give examples of its application to the analysis of force networks in dense granular media.