Brian Hepler
Brian Hepler

Mathematics Consultant

Download Resume
Interests
  • algebraic topology
  • differential equations
  • category theory
  • geometric deep learning
  • topological data analysis
  • quantum computation
Education
  • PhD Mathematics

    Northeastern University

  • MS Mathematics

    Northeastern University

  • BA Mathematics

    Boston University

My Research

I’m a research mathematician and educator with 13+ years of experience working at the intersection of abstract theory and practical computation. My expertise lies in relational structures, category theory, and topological methods, and I specialize in translating these concepts into efficient data models, algorithms, and mathematical infrastructure for machine learning and quantum computing.

I’ve published 5 peer-reviewed research articles and presented at over 20 international conferences. I’m actively building on my mathematical background to develop tools and frameworks that bridge theory and practice, with applications in machine learning, quantum computing, and data science.

I’ve also taught university-level mathematics for more than a decade, most recently designing and delivering a course on “Lie Groups with Applications” through Quantum Formalism Academy.

From 2023–2024, I was a postdoctoral researcher in the algebraic analysis group at IMJ-PRG (Sorbonne Université), working with François Loeser on the FSMP-funded project Condensed Mathematics, Ind-Sheaves, and Irregular Singularities. Before that, I held research appointments at UW–Madison, including a Van Vleck Visiting Assistant Professorship and a later honorary fellowship, collaborating with Laurentiu Maxim in geometry and topology.

I earned my Ph.D. from Northeastern University in 2019 under David B. Massey, with a dissertation on some invariants of complex analytic singularities titled “Hypersurface Normalizations and Numerical Invariants” (Read it here!).