Haoyuan Li - Data Science Summer Research Intern

Summary

Ph.D. candidate in Mathematics with experience developing machine learning and Topological Data Analysis models for anomaly detection, generative AI tooling, and complex data analysis. Skilled in Python, SQL, statistical modeling, persistent homology, and translating ambiguous technical problems into analytical workflows. Experienced in research, model prototyping, technical documentation, and communicating results to interdisciplinary audiences. Interested in building practical AI solutions that combine rigorous modeling, explainability, and business impact.

Work History

Data Science Summer Research Intern

Fitila Technologies

Chicago, Illinois

05.2024 - 08.2024

Built Python workflows for data preprocessing, feature construction, model experimentation, and visualization, supporting rapid prototyping of AI-driven analytical capabilities.
Developed components of generative AI analytics tool with Topological Data Analysis framework, applying persistent homology and anomaly-detection methods to uncover structural patterns in complex datasets.
Evaluated anomaly-detection approaches for financial time-series and network-style data, comparing methodological tradeoffs and documenting assumptions, limitations, and use cases for stakeholders.
Sourced and prepared open-access datasets for time-series forecasting, anomaly detection, and financial network analysis, improving the team’s ability to test model robustness across domains.
Authored technical documentation and research summaries that translated mathematical methods into actionable insights for product development and business strategies.

Education

Master of Science - Mathematics

SUNY At Binghamton

Binghamton, NY

05-2020

Bachelor of Science - Mathematics

China Agricultural University

Beijing

05-2017

Ph.D. - Mathematics

University of Illinois At Urbana-Champaign

Champaign, IL

05-2026

Skills

Programming & Data Analysis: Python, SQL, pandas, NumPy, statsmodels, Jupyter, data preprocessing, feature construction, data visualization
Machine Learning & AI: scikit-learn, PyTorch, TensorFlow, anomaly detection, time-series analysis, model evaluation, synthetic data validation
Generative AI & Advanced Analytics: generative AI tool development, Topological Data Analysis, persistent homology, high-dimensional data analysis

Software Engineering & Deployment: Git, APIs, Docker, reproducible workflows, technical documentation
Additional Tools: MATLAB, Mathematica, matplotlib

Projects

Bore Propagation / Numerical Modeling of Traveling Fronts

Developed a mathematical and computational framework to study fourth-order traveling-front equations arising in bore propagation.
Used Python-based shooting simulations to approximate heteroclinic connections between equilibrium states and evaluate convergence behavior.
Combined numerical evidence with analytical tools, including Green’s functions, invariant sets, barrier arguments, and Schauder fixed point theory.
Visualized solution trajectories and matching error to assess whether simulations supported the theoretical existence result.

Topological Data Analysis for Survey and Behavioral Data

Built Python scripts to convert high-dimensional questionnaire responses into topological representations for persistent homology analysis.
Used barcode summaries to detect stable geometric structures and relationships among survey items.
Created synthetic datasets with controlled labels to validate whether detected structures reflected meaningful signal rather than noise.
Visualized results and documented methodological assumptions for non-specialist audiences.

Quantum Computing / Entanglement Analysis

Developed Python tools to generate persistent homology barcodes from simulated quantum-state data.
Classified entanglement patterns and estimated associated probabilities using simulation-based workflows.
Combined mathematical modeling, numerical simulation, and data visualization to study structure in high-dimensional systems.

Finding the Math Department’s Deep Structure — Illinois Geometry Lab

Built Python-based visualizations to identify and communicate hidden structure among faculty research areas using phylogenetic-tree methods.
Translated complex relational data into clear visual outputs, helping nontechnical audiences understand patterns, clusters, and interdisciplinary connections.
Led undergraduate researchers through data preparation, analysis, and visualization workflows while providing hands-on Python troubleshooting and code review.

Publication

Boundedness of Marcinkiewicz integrals on Hardy spaces H^p over nonhomogeneous metric measure spaces, Journal of Mathematical Inequalities Li, Haoyuan & Lin, Haibo. (2018). 12. 347-364. 10.7153/jmi-2018-12-26.

Timeline