Much of my research is built on the idea that data has structure or “shape” and this shape helps us understand the data. For example, voting records may be clustered by party affiliation. In particular, the shapes I am most interested in are topological, like circles or voids (like the inside of a balloon). Detecting and measuring these types of shape can be difficult if the data is complex, that is, there are lots of different components (like many genes for many patients) or it changes over time (like a flock of birds).
As an illustration, suppose we have a set of points arranged very roughly in a circle. On their own, it’s just a bunch of points, but we can intuitively detect the structure, or how they interact with each other, by blurring our eyes until the points all merge into a ring. As a postdoctoral researcher in the Mathematics Department of the University of Arizona, my research uses math that makes this structure detection process precise for much more complicated data that evolves over time. This helps answer fundamental questions about the systems the data came from. For example, with collaborators, I find defects and measure order of arrays of nanodots as they form on semiconductors to better understand the process for potential in manufacturing. I characterize the roughness of snowfields as they melt to better estimate their energy transfer which is used in climate models. In another project we are studying the patchiness of coral reefs to better predict recovery and catastrophic reef loss. I love that math allows me to work on such a wide variety of scientific applications.
In addition to research, I have had the opportunity, with some colleagues in the math department, to launch a Women in STEM Mentorship Project this fall. This is a peer mentoring program for first year women in STEM majors. I am passionate about mentoring and making pathways for a more diverse STEM workforce.
Each month we'll feature a Postdoctoral Scholar and their research, sharing their experiences from the UA, life in Arizona and their research interests.