Jarvis Computational Mathematics Lab
Department of Mathematics, Brigham Young University
Principal Investigator: Tyler J. Jarvis, Professor of Mathematics
The Jarvis Computational Mathematics Lab, directed by Tyler J. Jarvis, develops rigorous mathematical and computational methods for real-world problems. Our work is currently organized around four research directions: numerical algebraic geometry, redistricting analysis, physiological signal processing, and generalized aliasing.
Research Directions
Numerical Algebraic Geometry
Developing fast, reliable numerical rootfinding methods for systems of polynomial and analytic equations, and the open-source Yroots software that implements them.
Redistricting Analysis
Applying mathematical and statistical methods to detect gerrymandering and evaluate the fairness of electoral district maps.
Physiological Signals
Mathematical modeling and signal-processing methods for periodic and pulsatile physiological signals, with applications to noninvasive health monitoring.
Generalized Aliasing
A new theoretical paradigm for understanding model complexity and generalization, explaining phenomena such as double descent and informing model design.
Numerical Algebraic Geometry
The lab develops numerical methods for finding all roots of systems of polynomial and analytic equations, with an emphasis on reliability, speed, and scalability to high dimensions. This work is implemented in Yroots, our open-source numerical rootfinding tool.
Redistricting Analysis
The lab studies the mathematics of political redistricting, developing quantitative tools to identify gerrymandering and to assess the fairness and compactness of proposed district maps.
- A. King, J. Murri, J. Callahan, A. Russell, and T. J. Jarvis, Mathematical Analysis of Redistricting in Utah. Statistics and Public Policy 9(1), 136–148 (2022).
- Tyler Jarvis was also a coauthor on an Amicus Curiae Brief of Mathematicians, Law Professors, and Students filed with the U.S. Supreme Court in Rucho v. Common Cause / Lamone v. Benisek (Nos. 18-422, 18-726), March 2019.
Physiological Signals
The lab develops mathematical models and signal-processing algorithms for analyzing periodic and pulsatile physiological signals (e.g., cardiac and respiratory waveforms, spectrometer signals), with applications to noninvasive health monitoring.
Generalized Aliasing
The lab is developing generalized aliasing as a new theoretical paradigm for understanding how model complexity relates to predictive performance. This framework explains phenomena such as double descent that are not well captured by the classical bias–variance decomposition, and it can inform model design and experimental design before data collection.
- M. K. Transtrum, G. L. W. Hart, T. J. Jarvis, and J. P. Whitehead, Generalized Aliasing Explains Double Descent and Informs Model Design. Physical Review Research 7, 043268 (2025).
People
Current Lab Members
- Hyun Lee
- Alice Lundgren
- McKayla Davis
- Aleena Cupp
- Quinn Oveson
- Justin Murri
- Andrew Swenson
- Ethan Foulke
- Joseph du Toit
- Eli Sampson
- Aiden Henrie
Faculty Collaborators
- Jared Whitehead
- Robert Davis
- Gus Hart
- Mark Transtrum
Funding
Research by the PI has been supported by federal grants for three decades, including:
- Tula Health, “Noninvasive health sensing” (2021–2025)
- National Science Foundation DMS-1564502, “Focused Research Group: Crossing the Walls in Enumerative Geometry” (2016–2020)
- National Science Foundation DUE-1323785, “TUES: A New Curriculum in Applied and Computational Mathematics” (2013–2017)
- National Science Foundation DMS-1148695, “Center for Mentoring Undergraduate Research in Mathematics” (2012–2017)
- National Security Agency H98230-10-1-0181, “Group Actions, Orbicurves, and Topological Field Theory” (2010–2012)
- National Science Foundation DMS-0636648, “Center for Mentoring Undergraduate Research in Mathematics” (2006–2010)
- National Science Foundation DMS-0605155, “Stringy Invariants, Orbicurves, and Topological Field Theory” (2006–2009)
- National Science Foundation DMS-0105788, “Higher Spin Curves and Cohomological Field Theories” (2001–2005)
- National Security Agency MDA904-99-1-0039, “Moduli of Higher Spin Curves” (1998–2000)
- National Science Foundation CAREER Award DMS-9501617, “Moduli of Generalized Spin Curves; Class Size and Calculus Learning” (1995–1998)
See the PI’s curriculum vitae for a complete list of funding, publications, and awards.
Contact
For questions about the lab, contact the principal investigator, Tyler J. Jarvis, Professor of Mathematics, Brigham Young University: jarvis@mathematics.byu.edu. Official profile: BYU Faculty Directory.