“Anyone can use mathematics to understand their scientific interests,” Robyn Brooks says. “Not just people who love calculus or statistics!”

As a postdoctoral fellow at the U, Robyn leads the Science Research Initiative (SRI) stream on topological data analysis (TDA).

“Computational topology is used to quantify the structural properties of shape,” says Robyn who received her BS from Trinity University in mathematics followed by a master’s degree in finance from the University of Colorado Boulder and a PhD in mathematics from Tulane University in 2020. “In particular, TDA allows us to find hidden shape patterns in data and use mathematics to analyze what these hidden patterns represent in the context of the data set.”

Robyn became interested in topology as a graduate student when she participated in workshops funded by the Association for Women in Mathematics and their program for advanced research networks. “The mathematics of TDA are very interesting,” states Robyn, “and the support of the network of women and non-binary mathematicians in topology helped me develop my collaboration and research skills, as well as providing me with inclusive and welcoming spaces to do mathematics.”

Her research within topology focuses on multi-parameter persistent homology, an area of TDA which assigns shape properties to data sets and provides analysis of these shape properties along different parameters. In her SRI stream the goal is to do novel research in both the theory and applications of TDA, developing math literacy skills such as reading, writing, and discussing quantitative topics.

For the adventurous young scientist, opportunities abound in her stream, including in TDA theory. Another involves creating and implementing algorithms in Python for the computation of mathematical invariants and quantitative summaries given by TDA.

Finally, there are opportunities for collaboration with other areas of science, to pose and investigate quantitative questions in different disciplines using TDA software

Amplifying voices of minorities

Robyn is on the organizing committee of two math conferences, Math For All and USTARS, or the Underrepresented students in Topology and Algebra Research Symposium, both of which are aimed at amplifying the voices of minorities historically excluded from mathematics. She also received the Outstanding Teaching Award from Tulane University in 2019.

“I am passionate about math education and encouraging women in the STEM fields,” says Robyn. She also believes that topology is important for everyone and can be used in many fields of science, not just mathematics.

“Computational topology can be used in a wide variety of applications — in scientific problems with numerical data, but also in problems where any kind of relationship between objects of interest is important. It provides mathematically rigorous measurements that can be used to understand these relationships and allows scientists to add the tools of mathematics to their problem solving arsenal.”

Her personal hero is Candice Price, an associate professor of mathematics at Smith College whose research focuses on DNA topology. Price is a co-founder of the Mathematically Gifted and Black (MG&B) Website and USTARS, as well as co-director of the Enhancing Diversity in Graduate Education (EDGE) Summer Program.

Originally from Salt Lake City, Robyn doesn't just assign shapes to data sets but also to her products that stem from interests outside of mathematics: quilting, sewing and knitting.