Northwestern’s ESAM PhD specializes in asymptotic analysis, stochastic modeling, and scientific machine learning to decode turbulence, epidemics, and neural computation. Students collaborate with climate scientists, biophysicists, and Wall-Street quants, publishing in *PNAS* and *SIAM Review*. Teaching fellowships and a policy communication practicum groom graduates for academia, national labs, and data-science leadership.
Derive homogenized models for porous-media flow with reactive fronts
Develop neural-operator surrogates for weather-prediction PDEs
Analyze metastability in stochastic epidemic networks with multiscale methods
Prove global existence for viscoelastic thin-film equations
Model swarm-robot consensus via mean-field control theory
Compute optimal transport metrics for fairness in reinforcement learning
Study soliton interactions in nonlocal nonlinear Schrödinger systems
Implement GPU-accelerated spectral solvers for rotating-stratified turbulence
Quantify systemic-risk contagion in interbank networks through random graphs
Optimize vaccine distribution under supply uncertainty with stochastic programming
Investigate pattern formation in chemotactic biofilms using bifurcation analysis
Apply rough-paths theory to volatility modeling in high-frequency finance
Construct Bayesian inverse-problem frameworks for seismic tomography
Simulate elastic-rod dynamics in soft-robot tentacle locomotion
Write an expository monograph on fractional-calculus applications in rheology
Advance mathematical frontiers and interdisciplinary discovery with Northwestern ESAM.
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