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Bradley Z. Vigil

Ph.D. Candidate in Mathematics | Applied Algebraic Topology

Bradley Z. Vigil studies complex systems through applied algebraic topology, using mathematical tools to understand what persists across data, patterns, and changing systems.

  • Degree: Ph.D. in Mathematics
  • Research Area: Applied Algebraic Topology
  • Expected Graduation: May 2026
  • Honors: United States Quad Academic Fellow; Charles S. Peirce Interdisciplinary Scholar
Portrait of Bradley Z. Vigil

Persistence as a Path

For Bradley, persistence has shaped both his personal journey and his academic work. As a first-generation Hispanic graduate student from West Texas, he credits the persistence of his family, mentors, and community with helping him build a path through higher education and research.

That same idea of persistence is central to his mathematical research. His work studies complex systems through persistent homology, a field that looks for meaningful structures that remain present across changing data.

Research in Plain Language

Bradley’s research develops mathematical tools for studying differences in complex systems. These systems may include brain activity during epileptic seizures, changes connected to neurodegenerative disease, or the spread of maladapted states through a population.

His work creates new mathematical lenses for understanding these systems by focusing on what remains stable or persistent. In Bradley’s words, the central idea is approachable: look at what persists, because persistence sets the course.

Graduate School Highlight Video

Bradley was also featured in a Texas Tech Graduate School highlight video discussing his research.

A Defining Accomplishment

Among the accomplishments Bradley holds closest is being selected as one of fifty students worldwide to receive the Quad Fellowship. For him, that recognition is a reminder that persistence, when guided by purpose, can carry students farther than they may have imagined.

“Success is not final, failure is not fatal: It is the courage to continue that counts.”
— Winston Churchill

Career and Future Goals

As Bradley completes his doctoral work, he is preparing to continue academic research while giving back to West Texas, the place he proudly calls home.

His experience at Texas Tech has been shaped by mentorship, opportunity, and the persistence of faculty who helped open new doors for his future research path.

Advice for Future Graduate Students

Bradley encourages prospective graduate students to trust the process, especially when the path feels uncertain. Growth in research, scholarship, and life rarely follows a straight line.

There will be moments when the problems feel larger than you, but persistence creates a path. Through that path comes progress, and through progress, new possibilities become visible.