About

I am a 4th-year applied mathematics Ph.D. student at the University of Colorado Boulder (CU Boulder), where I am advised by Adrianna Gillman. My research interests are broadly in numerical partial differential equations and applications of functional, numerical, and asymptotic analysis techniques. In particular, I enjoy working on boundary integral equations methods for elliptic PDE and designing associated “fast” algorithms. I received bachelor's (BSc) and master's (MS) degrees in applied mathematics from CU Boulder and am expected to graduate from the doctoral program in May of 2028. For more on my professional experience, please see my CV: PDF

Outside of teaching and research, I enjoy serving as the president of CU Boulder's Society for Industrial and Applied Mathematics (SIAM) Graduate Student Chapter, which hosts regular graduate student and alumni talks aimed at fostering interconnectedness in research amongst graduate students. I also enjoy trail running and rock climbing in and around Boulder, CO.

Publications

  1. Trujillo, M.; Sajadi, A.; Shaw, J. D.; Hodge, B.-M., Computationally Efficient Analytical Models of Frequency and Voltage in Low-Inertia Systems, IEEE Transactions on Power Delivery 2026 arXiv
  2. Trujillo, M.; Sajadi, A.; Shaw, J. D.; Hodge, B.-M., Analytical Models of Frequency and Voltage in Large-Scale All-Inverter Power Systems, IEEE Transactions on Power Systems 2025 arXiv
  3. Shaw, J. D.; Restrepo, J. G.; Rodríguez, N., A dynamical system model of gentrification: Exploring a simple rent control strategy, Phys. Rev. E 2024 arXiv

Talks

  • Correcting the density interpolation method (DIM) for boundary integral equations, SIAM Graduate Student Chapter Seminar, University of Colorado Boulder, January 2026 (contributed talk)
  • A dynamical system model of gentrification: Exploring a simple rent control strategy, Complex/Dynamical Systems Seminar, University of Colorado Boulder, March 2025 (invited talk)
  • A dynamical system model of gentrification: Exploring a simple rent control strategy, Dynamics Days US 2025, January 2025 (contributed talk; travel award recipient)
  • On the dynamics of gentrification, Mathematical Biology Seminar, University of Colorado Boulder, October 2023 (contributed talk)

Teaching

I have served as a teaching assistant for the following courses at CU Boulder:

Software