I am an Assistant Professor of Mathematics in Portland State University's Fariborz Maseeh Department of Mathematics + Statistics. 

Research

My research lies at the intersection of computational mathematics, partial differential equations, network science, and public health applications. My work combines numerical analysis, PDE theory, and network-based modeling to study how structure and geometry influence dynamical behavior. Representative scholarship is provided below. For a full list of papers, please see my Google Scholar page.

• Metric graphs: Building on my 2022 dissertation on numerical methods for metric graphs, I continue to develop numerical methods and mathematical theory for PDEs on these structures. My interests include numerical methods for eigenvalue problems, spectral properties of metric graphs (such as distribution of eigenvalues, localization, and steady-state behavior), and applications to epidemiology and optical science.

  • • Brio, Caputo, Kravitz. Spectral Solutions of PDEs on Networks. Applied Numerical Mathematics, 2022.

    • Kravitz, Brio, Caputo. Localized eigenvectors on metric graphs. Mathematics and Computers in Simulation, 2023.

• Mathematical epidemiology: I study how population movement along network structures (such as road networks, airline networks, and river networks) affects the geographic spread of disease. My work emphasizes PDE-based models with the goal of understanding how particular structures within networks enhance or inhibit transmission.

  • • Kravitz,  Durón, Nieves, Brio. Data-driven Optimization and Parameter Estimation for a Metric Graph Epidemic Model with applications to COVID-19 spread in Poland: A real-world example of optimization for a challenging Rosenbrock-type objective function. An International Journal of Optimization and Control: Theories & Applications, 2025.

    • Durón, Kravitz, Brio. Edge percolation centrality: A new measure to quantify the influence of edges during percolation in networks. PLoS One, 2025.

• Coupled ODE+1D+2D systems: I develop and analyze coupled systems in which the vertices are modeled using time-dependent ODEs, the edges by one-dimensional PDEs, and the surrounding regions by two-dimensional continuum models. In this framework, each nth dimensional component acts as a boundary for the (n+1)st dimension, leading to novel numerical and analytical challenges, as well as flexible modeling capabilities for multiscale systems.

  • • Kravitz, Durón, Brio. A Coupled Spatial-Network Model: A Mathematical Framework for Applications in Epidemiology. Bulletin of Mathematical Biology, 2024.

• Numerical methods for irrational rotations: I recently developed a numerically stable algorithm that computes the discrepancy of an irrational rotation exactly (up to machine precision) over its entire domain). By tracking the discontinuities rather than relying on sampling, this approach allows the exact computation of the support of the distribution over a large number of term, allowing us to deduce patterns that were previously inaccessible computationally.

  • • arXiv Preprint: Kravitz, Computational study of irrational rotations via exact discontinuity tracking, 2025.