My current research is focused on using the finite element method to rigorously estimate the Hausdorff dimensions of fractals produced by continued fraction iterated function systems. In particular, I use B-spline quasi-interpolants, which provide reliable, high-order estimates that also have rigorous mathematical justifications.
My other interests, which I focused on during my undergraduate career (but still enjoy!), include dynamical systems, network science, and combinatorics.
Adam Giammarese, Jacob Brown, and Nishant Malik. Reconfiguration of Amazon’s connectivity in the climate system. Chaos: An Interdisciplinary Journal of Nonlinear Science, 34(1):013134, 23 Jan 2024. Link
Jacob Brown. Counting divisions of a 2×n rectangular grid. The College Mathematics Journal, 54(3):212–221, 03 May 2023. Link
Rigorous High-Order Hausdorff Dimension Estimation of Limit Sets of Continued Fraction Iterated Function Systems via B-Splines
Math Chat Seminar, Bridgewater State University
Rigorous, High-order Dimension Estimates for Limit Sets of Continued Fraction Iterated Function Systems using B-splines (April 6, 2026)
AMS 2025 Fall Eastern Virtual Sectional, Virtual
A B-spline based finite element approach for estimating the Hausdorff dimensions of infinite
subsystems of continued fractions (October 25, 2025)
Finite Element Circus, Tufts University
Rigorous, High-order Dimension Estimates for Limit Sets of Continued Fraction Iterated Function Systems using B-splines (April 25, 2026)
New York State Regional Graduate Mathematics Conference, Syracuse University
A B-spline based finite element approach for estimating the Hausdorff dimensions of continued fraction iterated function systems (March 21, 2026)
Workshop in PDE and Applied Math in the Northeast Region, University of Connecticut
A B-spline based finite element approach for estimating the Hausdorff dimensions of continued fraction iterated function systems (March 7, 2026)
SIGMA Seminar, University of Connecticut
Analysis of the Amazon Rainforest via Climate Network Theory (April 5, 2024)
MAA Mathfest, Virtual
Counting Divisions of a 2 × n Grid (August 7, 2021)