Kate Pearce Awarded NSF-DMS Ascend Postdoctoral Fellowship

The allure of superheroes with double lives captivate society’s collective imagination - from Peter Parker swinging between the responsibilities of high school and saving cities as Spiderman, to Clark Kent’s transformation from a mild-mannered accountant to Metropolis’ resident protector. 

Here at the Oden Institute of Computational Sciences and Engineering, postdoctoral researcher Kate Pearce lives a double life of her own. By day, she works as a postdoctoral fellow at the Center for Numerical Analysis, researching rank-structured matrix compression. By night, she serves as an advocate for bringing mathematics education to Lockhart Correctional Facility - teaching college-credit bearing courses through the Texas Prison Education Initiative that seek to target the systemic inequities that incarcerated women face in terms of access to STEM education. 

This year, Pearce was awarded the NSF-DMS Ascend Postdoctoral Fellowship, a program designed to support and provide funding to researchers who will broaden the participation of groups that have been historically excluded from, or are currently underrepresented in STEM fields, while pursuing their postdoctoral research. 

This fellowship allows Pearce to continue her work with Oden Institute core faculty member Per-Gunnar Martinsson on rank-structured matrix compression. “Modern computer architectures allow us to solve increasingly large and complex problems in scientific computing,” Pearce shared, “and many of these problems require the application of algorithms  from numerical linear algebra.” However, as datasets get larger and more complex, with up to billions of degrees of freedom, computational performance is capped by algorithmic complexity and becomes bottlenecked by the inefficient use of computational resources. 

This makes it essential to find ways to effectively compress large matrices. “Many matrices in scientific computing have an exploitable low-rank structure,” said Pearce. This means that these matrices  can be compressed without losing critical information. This matrix structure is seen across mathematical disciplines, ranging from covariance matrices in statistics, to kernel matrices in machine learning.

Pearce’s research focuses on developing randomized algorithms that exploit  the low-rank structure of these matrices,  invoking a process called randomized sketching. In randomized sketching, the row or column space of a (typically large) matrix is approximated by analyzing how the matrix acts on smaller matrices drawn from random distributions. Dense algorithms from numerical linear algebra can then be applied to compress the smaller randomized sketch in lieu of the original matrix, yielding a high-quality approximation at a greatly reduced computational cost.  The compressed  matrix representation can be used to perform ubiquitous numerical operations efficiently, including factorization, spectral decomposition, and inversion, giving us insight into the behavior of the original, much larger, dataset, without a significant loss in accuracy.  

As Pearce builds strategies to make inscrutable matrices analyzable, she also works to demystify the world of learning mathematics to incarcerated students at Lockhart Correctional Facility. Her courses are run through the Texas Prison Education Initiative (TPEI), a volunteer-driven program run through UT Austin’s Department of Sociology.

Pearce pioneered TPEI’s first pre-calculus course, and created materials specifically suited for teaching students within the prison system. “We live in a world surrounded by technology, but it isn’t accessible given the constraints we’re working with in a prison setting,” Pearce shared. As the program is donation funded, items many readers have relied on through our mathematics education become inaccessible - including textbooks, electronic resources, and access to instructors outside of class time.

“This grant will make a world of difference,” Pearce shared excitedly. “We’re finally able to buy math textbooks for our students, and I have dedicated time for course creation and development . We’re also now  able to reimburse  instructors for their travel costs in getting  to the facility in Lockhart, which helps make this teaching opportunity significantly more manageable for busy graduate students.”  

Beyond changes in teaching methods to accommodate for the inherent structural challenges surrounding prison education, Pearce found that many students came into her courses with an inbuilt trepidation surrounding math conceptually. “The last time many of our students were exposed to math was in middle or high school - they’re coming from a background of deeply inequitable education access, and many believe that math just isn’t something they’re good at - which couldn’t be further from the truth,” Pearce stated.

She has witnessed their ability to appreciate high-level mathematical concepts many times during “The Art of Mathematics,” a non-credit bearing course Pearce taught through TPEI, which explores the relationship between these seemingly disparate concepts. “We talk about logic, incompleteness, abstraction, randomness, and non-Euclidean geometry,” Pearce said. “You don’t get to explore concepts like that in high school. So many of my students are talented artists. When they see how math plays into a passion they have, it gets so much more accessible. Teaching this course has been one of my greatest joys - there’s nothing more rewarding than when a student who’s never felt confident surrounding math tells you that they feel like a mathematician.”

Now, Pearce aims to expand TPEI’s course offerings to allow students to study advanced content - including calculus and discrete mathematics. This sets the stage for the development of problem solving skills, as well as progress towards STEM degrees post-incarceration with  UT Austin accredited courses.

“None of this would be possible without the support I’ve gotten from both the Oden Institute and TPEI,” Pearce said. “Gunnar Martinsson and Karen Willcox have been instrumental in making my research possible, while TPEI leaders Sarah Brayne, Max Lubbell, Chloe Craig, and my co-instructors, especially Emily Hsiao, have been absolutely critical to my outreach work for this fellowship. I couldn’t be more grateful.” 

As she seeks to expand TPEI’s course offerings through her NSF Fellowship, Pearce notes that volunteer support is more critical than ever before. “If anyone is interested in getting involved, we’d be so  excited to have you on the team,” she shared. “Graduate students, postdoctoral researchers, and faculty members interested in teaching and outreach are always beyond appreciated. It’s a great opportunity  to gain teaching experience in a supportive and non-traditional setting. We’re also always looking for undergraduate students who can serve as remote teaching assistants.” 

As Pearce dedicates herself to improving accessibility in her scientific and outreach-driven work, she finds joy in the impact she’s creating - both at the Oden Institute and beyond it. 

Interested volunteers may contact Pearce here. For more information about prison education, refer to TPEI’s website.