The math underneath the infrastructure. PDE analysis, spectral theory, and scientific ML — supervised by Prof. Miao-Jung Yvonne Ou at the University of Delaware, and the same toolkit I'm shipping into SUM Innovation's decentralized inference stack.
Collapsing fine-scale periodic structure into effective macroscopic operators — capturing the physics that matters and dropping the rest. The compression theory behind every reduced-order system.
What the spectrum of an elliptic PDE does as the period parameter ε → 0. Spectral gaps, limit operators, and the analytic backbone of multiscale modeling.
Reduced-order models for systems where full-resolution simulation is impossibly expensive — same principle that lets a sharded LLM run across consumer hardware instead of a hyperscaler rack.
Wiring classical homogenization into generative models to reconstruct fine-scale structure from coarse signals. The bridge from PDE theory to data-driven systems that actually ship.
Earlier work — deterministic compartmental models, sensitivity analysis, reproduction numbers. How outbreaks propagate, and how to reason about them under uncertainty.
My dissertation digs into the asymptotic spectral properties of elliptic PDEs with periodic coefficients. As the period parameter ε → 0, the operator's spectrum develops structure — gaps, accumulation points, limiting behavior — that classical homogenization sees in silhouette but doesn't fully resolve. I use asymptotic analysis, functional analysis, and operator theory to pin it down.
The longer arc: take what spectral theory teaches us about coarse-from-fine reconstruction and turn it into machinery for data-driven multiscale modeling. That arc is also why SUM Innovation exists — efficient, verifiable inference on heterogeneous hardware needs the same compression instincts.
Brin Mathematics Research Center · University of Maryland
Week-long deep dive into ML methods for scientific computing and PDE-constrained problems. Half the toolkit feeding directly into the OmniNode inference layer.
Nigerian Association of Mathematics Sciences Students · Abuja
Society for Mathematical Biology
NYA