Co-Directors: Michael Kirby, Professor of Mathematics, and Chris Peterson, Professor of Mathematics
Department of Mathematics
Colorado State University
Mathematics and the study of patterns
The Pattern Analysis Laboratory supports faculty and student research in the Department of Mathematics at Colorado State University. Our work applies fundamental mathematical theory, particularly differential geometry and topology, to understand the structure of data residing in spaces of large ambient dimension.
The analysis of patterns in data has traditionally been a subject in statistics and engineering. The research at the laboratory emphasizes the transition of mathematical theory to efficient algorithms, and it is remarkable how a single mathematical framework can find applications across an array of seemingly disparate problems.
Areas of research
- Representation of data on Grassmann, Stiefel and flag manifolds
- Geometric optimization
- Computational geometry and topology
- Low-dimensional embeddings
Support
The Pattern Analysis Laboratory has been made possible by sustained support from the Department of Mathematics and the College of Natural Sciences at Colorado State University. We have also received support from other sources including the National Science Foundation, the Air Force Office of Scientific Research, the Defense Advanced Research Projects Agency, Honeywell, IBM, Siemens and the United States Forest Service. .