A mathematician who builds at the intersection of abstract theory and production code. I model real-world problems as graphs, solve them with algorithms, and deploy them as scalable systems. Every function I write is a theorem. Every test is a proof. Every deployment is a publication.
| Domain | Focus Area | Key Tools |
|---|---|---|
| Graph Theory | Network analysis, centrality, shortest paths, coloring | Neo4j, Cypher, NetworkX |
| Linear Algebra | Matrices, eigenvalues, SVD, PCA, spectral methods | NumPy, SciPy, TensorFlow |
| Probability & Statistics | Bayesian inference, hypothesis testing, estimation | R, scipy.stats, Pandas |
| Optimization | Convex optimization, gradient descent, LP/QP | TensorFlow, CVXPY |
| Numerical Methods | ODE/PDE solvers, interpolation, quadrature | SciPy, NumPy |
| Information Theory | Entropy, KL divergence, mutual information | NumPy, TensorFlow |
My research lives at the intersection of mathematical modeling, graph-based machine learning, and computational statistics. I explore how graph structures can capture complex relational patterns that traditional tabular data models fail to represent, then build production systems from those insights.
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Graph Neural Networks (GNNs) -- Learning from relational data structures using message passing and graph convolution operations on Neo4j-stored graphs. Building end-to-end pipelines from raw graph data to actionable predictions with interpretable results.
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Statistical Hypothesis Testing -- Rigorous validation with proper significance levels, confidence intervals, and effect sizes using R. Ensuring every research claim is backed by sound statistical evidence rather than mere correlation.
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Dimensionality Reduction & Embeddings -- PCA, t-SNE, UMAP for high-dimensional mathematical data visualization and feature engineering. Transforming abstract mathematical spaces into interpretable low-dimensional representations.
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Optimization Theory -- Gradient descent variants, convex optimization, and their applications in training deep learning models efficiently. Bridging the gap between theoretical convergence guarantees and practical training speed.
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Bayesian Inference -- Probabilistic programming, prior/posterior analysis, and MCMC sampling for uncertainty quantification in predictions. Moving beyond point estimates to full distributional understanding of model outputs.
"Mathematics is not about numbers, equations, or algorithms: it is about understanding." — William Paul Thurston
"The only way to learn mathematics is to do mathematics." — Paul Halmos
"Pure mathematics is, in its way, the poetry of logical ideas." — Albert Einstein
"Mathematics is the queen of the sciences and number theory is the queen of mathematics." — Carl Friedrich Gauss