Topological Data Analysis
Topic description: The analysis of high dimensional data sets requires non-traditional techniques to overcome fundamental computational limitations. Current work in this area involves the interaction of ideas from fields including data analysis, imaging, statistics, and topology. One approach to studying specific high dimensional systems is to run simulations of the behavior of a set of points in a mathematical model or to take a series of measurements of a physical system. The resulting data may then be studied via standard techniques of time series analysis, which involve computing statistical properties of the time series data in the hope of uncovering internal structures or trends. An alternative approach would be to use an topological tools to construct a useful mathematical model of the underlying system.
Research opportunities: A project in times series analysis and possible extensions based on topology would offer a good research opportunity for an advanced undergraduate. The student would begin by learning and implementing traditional statistical techniques in high demand in the field of data analysis. Since one of the goals of this work is to analyze data from physical systems, this project also provides a direct link to collaborations with researchers in the physical sciences.
Suggested prerequisites: Math 413-414, Math 426, experience with Matlab, C++
Contact: Sarah Day