Mathematics · Machine Learning · Systems

Structure,
found in chaos.

I'm Nicholas Tavares, a graduate mathematician who builds research code that gets validated and infrastructure that runs itself.

Network topology of markets under stress. A from-scratch autodiff engine. A deliberation protocol for panels of language models. GPU fractals. A deckbuilder about rigging slot machines. It all connects, I promise.

background: Julia set, z → z² + c, c orbiting the cardioid
rendered live on your GPU · little sibling of the Fractal Madness project
01 / About

Where pure math meets messy data

I'm a mathematician and ML engineer who builds systems that find structure in chaos. My academic work sits at the intersection of graph theory, information theory, and network analysis, using tools from pure mathematics to study complex systems and multi-agent architectures.

I recently finished my M.S. in Mathematics. A lot of my research keeps circling one question: whether the network topology of markets genuinely reorganizes under macroeconomic stress, or whether that structure is mostly hindsight. It's an open problem, and it deserves rigor, not vibes.

The rest of my time goes to building. Lately that ranges from an automatic differentiation engine written from scratch to prove I understand the chain rule, to a deliberation protocol for panels of language models, to a raymarcher that renders 4D fractals in real time. I believe the best insights come from asking better questions, not running faster models.

Education

Stevens Institute of Technology
M.S. Mathematics · Dec 2023 to Jun 2026
Oregon Institute of Technology
B.S. Applied Mathematics · 2015 to 2018

Elsewhere

GitHub ↗
Open source: Quorum, nabla, forecast-compare
LinkedIn ↗
Professional background
02 / Disclosures

Read this first

Short version: personal site, academic work, nothing here tells you what to do with money.

Personal Site

This website is maintained in my personal capacity only. It is not affiliated with, endorsed by, or associated with any employer or financial institution. All views and opinions expressed here are my own and do not represent the views of any firm. For professional background, see my LinkedIn profile.

Not Investment Advice

Nothing on this site constitutes investment advice, a solicitation to buy or sell securities, or a recommendation of any investment product, strategy, or course of action. All content is for educational and academic research purposes only and should not be used as the basis for any investment decision.

Research Disclaimer

All research findings, statistical results, and quantitative analysis presented here are theoretical and academic in nature. Historical patterns observed in specific datasets do not predict future performance and have not been validated for real-world application. Past performance, whether simulated or backtested, does not indicate future results.

03 / Research

The thesis

Publication-track quantitative research with novel mathematical contributions.

Network Theory Information Theory Geopolitical Finance HMM Regime Detection

Dynamic Multi-Asset Portfolio Topology Reorganization During Geopolitical Stress

N. Tavares, A. Hanini, B. Dasilva · Stevens Institute of Technology · 2025 to 2026
View on GitHub ↗

A framework for how multi-asset portfolio structures reorganize during geopolitical crises. It constructs multi-layer similarity networks across 91 ETFs in 8 asset classes using shrinkage correlation, distance correlation, and tail-dependence measures, then applies Leiden community detection, Hidden Markov Model regime identification, and information-theoretic tools (transfer entropy via the KSG estimator, Granger causality) to reveal directional information flow between asset clusters.

91ETFs analyzed
8asset classes
5novel metrics
24publication figures
6validation methods

Key findings

In this dataset, topology metrics showed structural changes preceding observed crises. A pattern that merits further study, not a forecast.
Tail-dependence CMI Granger-causes Pearson CMI (p = 0.041) in the sample period. Generalizability is under investigation.
The Treasury cluster shifted to primary information sender during the geopolitical periods studied, versus credit in calm regimes.
COVID showed distinct cluster dissolution (CMI = 1.0) with faster structural recovery than geopolitical shocks.

Novel contributions

CMI (Cluster Migration Index) TDS (Topology Deformation Score) Layer Agreement Metric Net Transfer Entropy Ranking Cross-Layer Granger Causality

Methodology and robustness

Walk-Forward Validation Block Bootstrap CI IAAFT Surrogate Testing Monte Carlo Power Analysis Bonferroni & BH-FDR Correction Sensitivity Analysis
Academic research: findings above come from a specific historical dataset and time period. They have not been validated for real-world application and should not be read as investment recommendations.
04 / Projects

Things I've built

Research systems, open source libraries, agents, graphics, and one video game.

This list writes itself. A pipeline on my machine scans the local repos twice a day, pulls live git stats, runs a safety filter over every description, and republishes the JSON this page reads. New work shows up here when it's real, not when I remember to edit HTML.

05 / Mathematics

The foundation

From abstract structures to applied algorithms.

06 / Experience

The path so far

2025 to present

Quantitative Researcher & ML Engineer

Stevens Institute of Technology / Independent

Researching multi-asset topology dynamics during geopolitical crises and developing novel metrics (CMI, TDS) with full statistical robustness validation. Building multi-agent research systems for prediction market data, and releasing open source along the way: a multi-model deliberation engine, a from-scratch autodiff library, and a forecast comparison toolkit.

Graph Theory Transfer Entropy HMM Multi-Agent Systems Open Source
2023 to 2026 · completed

M.S. Mathematics

Stevens Institute of Technology

Coursework in Machine Learning (CPE595), Applied Statistics (MA544), Time Series Analysis (MA641), Optimization & Stochastic Calculus (MA576), and Big Data Technologies (BIA678). Thesis on multi-asset network topology under macroeconomic stress, plus research projects that bridge academic rigor with working software.

LSTM SARIMA HMM Spark Kafka PostgreSQL
07 / Contact

Get in touch

Open to academic research collaborations, quantitative mathematics discussions, and software engineering opportunities. If you're working on interesting problems at the intersection of mathematics and computation, I'm happy to connect.