About me
I am a Ph.D. student in Mathematics at George Mason University, working under the supervision of Dr. Harbir Antil. My current research develops convex-duality methods and a posteriori error estimates for constrained PDE problems, including obstacle problems, flux-constrained flows, and curl–curl Maxwell systems with pointwise field bounds.
Before joining GMU, I completed Universidad Técnica Federico Santa María’s six-year integrated Mathematical Engineering program (B.Sc. awarded in 2020, professional degree in 2023) together with an M.Sc. in Mathematics (2021–2023) under the supervision of Dr. Leonelo Iturriaga. The M.Sc. is part of the same integrated program and shared a single thesis defense with the engineering degree.
Research interests
My broader interests sit at the intersection of nonlinear analysis and numerical analysis of partial differential equations:
- Nonlinear PDEs. Existence and multiplicity of solutions via variational techniques (Mountain Pass and linking theorems), fixed-point methods, and sub- and super-solutions. I have worked most extensively with the $p$-Laplace operator under both homogeneous and nonhomogeneous Dirichlet boundary conditions.
- Numerical analysis and optimal control of PDEs. Convex duality methods, finite element methods, a posteriori error analysis, obstacle problems, and PDE-constrained optimization on graphs.
News
- Nov 2025 — Preprint posted on arXiv: Optimal Boundary Control of Diffusion on Graphs via Linear Programming (with H. Antil and R. Löhner). arXiv:2511.03129
- 2025 — Presented at the Finite Element Circus at George Mason University.
- 2025 — Invited speaker at the Seminar on Calculus of Variations, Georgetown University.
- 2025 — Poster at IMSI, University of Chicago: Optimal Control and Decision Making Under Uncertainty for Digital Twins.
- 2026 — Poster at ICERM, Brown University: Simulation-Based Optimization with Applications.