My research falls in a young and exciting area of mathematics known as applied topology. In recent years, researchers have applied topological methods to solve problems in engineering, computer science, biology, and other areas. Much of the success in these applications results from the use of topology to organize and analyze data.
The goal of my research is to develop mathematical, and especially topological, tools for data analysis. Within my research program, I have three focus areas:
Click the links above to read more about each of my focus areas. Also, see my papers and presentations.
Hadwiger Integration of Random Fields: I provide a formula for the expected values of Hadwiger integrals (and, using Hadwiger's Theorem, more general valuations) of Gaussian-related random fields, which are both theoretically interesting and potentially useful in applications such as sensor networks and image processing. (Published in Topological Methods in Nonlinear Analysis, 2015.)