Fatim Majumder | Applied Mathematics / Machine Learning PhD Applicant
Incoming Columbia M.S. in Applied Mathematics, Fall 2026. Emory B.S. in Computer Science and Mathematics, expected May 2026.
I work on reliable empirical ML, scientific computing infrastructure, optimization, statistical model comparison, uncertainty-aware decision-making, and AI for science.
Guiding Thesis
Modern ML systems should be treated as scientific instruments: calibrated, auditable, stress-tested, falsifiable, and reproducible.
About / Research Profile
I am an applied mathematics and machine learning researcher building reproducible computational systems for model evaluation, scientific inference, and uncertainty-aware decision-making.
I turn informal empirical ML questions into controlled numerical experiments with explicit data-generating assumptions, artifact provenance, calibrated uncertainty, numerical stability checks, and statistically valid comparisons.
My research direction spans reliable AI for science, robust optimization, uncertainty quantification, graph-structured inference, differentiable simulation, and evaluation methods for foundation models.
Education
Columbia University | New York, NY
Incoming Fall 2026.
Planned focus: numerical analysis, scientific computing, stochastic processes, optimization, inverse problems, probabilistic modeling, statistical inference, and mathematical machine learning.
Emory University | Atlanta, GA
Expected May 2026. GPA: 3.98/4.00 cumulative; 4.00 mathematics; 4.00 computer science.
Research Interests
Statistical learning theory, calibration, conformal prediction, robustness, model selection, representation learning, graph learning, distribution shift, and benchmark validity.
Stochastic approximation, adaptive first-order methods, mirror descent, momentum, preconditioning, constrained optimization, inverse problems, and PDE-constrained learning.
Numerical linear algebra, Krylov methods, state-space inference, differentiable simulation, surrogate modeling, uncertainty quantification, active experimentation, and structure-aware neural systems.
LLM evaluation, tool-use and retrieval benchmarks, agent reliability, artifact lineage, dataset/version control, inference orchestration, auditability, observability, and failure-mode analysis.
Experience
These roles are presented for the methods they required: reproducible experiments, statistical validation, lineage-aware infrastructure, and careful model comparison.
Selected Projects
The project archive emphasizes benchmark design, leakage-aware validation, robustness testing, state-space simulation, and reproducible empirical workflows.
Generative audio robustness
Full-stack benchmark platform for generative audio models with 18,000+ controlled robustness runs, 82 perturbation operators, 9 evaluator families, deterministic manifests, and signal-level, perceptual, and model-based metrics.
Read case studyGraph learning
Heterogeneous spatiotemporal graph prediction over 1.1M+ collision records and road-network topology, improving hotspot-ranking AUROC by 23.4 points and top-decile recall by 31% with leakage-aware validation.
Read case studyState-space estimation
Modular localization simulation comparing standard Kalman filtering with robust variants under sensor dropout, delayed observations, outlier regimes, correlated process noise, and measurement misspecification; median error fell 49%.
Read case studyQuantitative research
Public-facing factor research and backtesting demo with point-in-time ingestion, signal construction, portfolio formation, evaluation, transaction-cost modeling, benchmark comparison, attribution, and reproducible tearsheets.
Read case studyNotes / Writing
These notes emphasize derivation, geometric intuition, computational experiments, and failure cases.
in progress
Mirror descent, momentum, stochastic approximation, and control-oriented views of optimization.
draft
Spectral structure, conditioning, approximation, and the numerical behavior of ML computations.
draft
Road networks, spectral graph structure, message passing, retrieval, and representation learning.
draft
Generative modeling, stochastic processes, denoising objectives, and computational failure modes.
outline
Probabilistic modeling, derivative observations, covariance structure, and smoothness assumptions.
outline
State-space estimation under misspecification, delayed observations, outliers, and dropout.
Honors / Leadership
Technical Skills
Python, C++, C, SQL, TypeScript, JavaScript, Java, Bash, MATLAB, LaTeX
PyTorch, JAX, PyTorch Geometric, scikit-learn, XGBoost, statsmodels, Ray, LLM evaluation, graph ML, multimodal ML, transformer inference, retrieval evaluation, robustness testing, ablation studies, uncertainty estimation
Numerical linear algebra, Krylov methods, preconditioning, convex/numerical optimization, stochastic approximation, state-space models, Kalman filtering, Monte Carlo simulation, Bayesian inference, statistical learning, spectral methods, graph algorithms
PostgreSQL, MySQL, DuckDB, Redis, Kafka, Airflow, dbt, ETL/ELT, dataset versioning, artifact lineage, experiment tracking, reproducible replay, structured logging
FastAPI, Docker, Kubernetes, AWS, Linux, Git, GitHub Actions, CI/CD, distributed queues, async orchestration, caching, batching, observability, profiling
Benchmark design, metric validation, regression detection, prompt/dataset lineage, statistical comparison, confidence intervals, run-diff tooling, audit logs, failure analysis, incident triage, model-risk documentation
Contact
I am especially interested in research mentorship and projects at the intersection of applied mathematics, mathematical ML, optimization, scientific computing, AI for science, statistical evaluation, and reliable AI systems.