Thomas Wanner, PhD

Research Focus

My research is generally concerned with dynamical processes, as modeled for example by partial differential equations, as well as deterministic and stochastic dynamical systems. My research focus has been on models arising in materials science, and I have used topological as well as rigorous numerical tools to study their dynamics. In addition, I have developed and used tools for topological data analysis.

Current Projects

■ Computer-assisted study of dynamical models. Focus is on their bifurcation structure and long-term dynamics. The methods are based on numerical computations, mathematical fixed-point theorems, and validation via interval enclosure methods.

■ Development of combinatorial tools for the topological analysis of dynamical systems. Focus is on combinatorial vector fields and their generalizations, index theory, computational homology, and persistence.

■ Topological data analysis of complex evolving patterns. Focus is on the use homology and persistence methods to develop topological signatures which can be used for pattern classification.

Select Publications

■ P. O’Neil and T. Wanner. Analyzing the squared distance- to-measure gradient flow system with k-order Voronoi diagrams. Discrete & Computational Geometry 61(1), 91-119 (2019).

■ T. Wanner. Computer-assisted bifurcation diagram validation and applications in materials science. Proceedings of Symposia in Applied Mathematics, American Mathematical Society, Providence (2018).

■ J.L. Chan et al., Challenges to transforming unconventional social media data into actionable knowledge for public health systems during disasters. Disaster Medicine and Public Health Preparedness, 1-8 (2019).