Harvard’s Applied Mathematics PhD empowers theorists and practitioners to invent algorithms that decipher neural codes, turbulence cascades, and market instabilities. Students craft cross-disciplinary plans with genomics, climate physics, or econ departments, publishing in *Science* and deploying open-source solvers on cluster GPUs. Graduates pioneer quantitative breakthroughs in academia, finance, and tech.
Sparse-tensor solvers accelerating large-scale climate models
Optimal transport frameworks for fair machine-learning algorithms
Neural-stochastic differential-equation model of brain calcium waves
Game-theoretic analysis of renewable-energy market auctions
GPU-accelerated Lattice Boltzmann simulation of blood micro-flow
Deep-reinforcement learning controller for fusion-plasma confinement
Mathematical proof of stability bounds in generative diffusion models
Bayesian calibration of ice-sheet tipping-point parameters
Agent-based model coupling epidemiology with misinformation spread
Thesis on topology-driven methods in high-dimensional data clustering
Interactive visualization library for teaching chaos theory
Open-source package implementing fractional-order PDE solvers
Capstone workshop on ethics of algorithmic decision-making
Invent mathematical tools that illuminate and reshape complex systems.
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