Tech’s Applied Math PhD blends proof rigor with computational horsepower. Doctoral scholars may formalize topological quantum-error codes, craft multigrid solvers for exascale climate models, or derive stochastic controls for autonomous swarms—often collaborating with Sandia, CDC, or Two Sigma.
Optimal transport on manifold learning for fairness metrics
Hybridizable discontinuous-Galerkin schemes for shallow-water equations
Homology-based anomaly detection in power-grid phasor graphs
Stochastic control of mean-field games in traffic flow
Proof-assistant formalization of primality test complexity
Sparse FFT algorithms for compressive seismic imaging
Bayesian inverse problems in geothermal reservoir modeling
Random-matrix universality in mmWave channel capacity
Neural-PDE surrogates with provable error bounds
KAM-theory extension to non-Hamiltonian biological oscillators
Multi-level Monte Carlo for options under rough volatility
Coupled bulk-surface PDEs for tumor growth interfaces
Integer-programming relaxations for genomic haplotype assembly
Topology optimization under uncertainty for metamaterial design
Computational homotopy in robot motion-planning manifolds
Discover mathematics that powers tomorrow’s breakthroughs.
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