About

I’m a researcher in computational mathematics and data science. My specialties are symbolic computation, constructive real algebraic geometry, and mathematical software development. I am especially interested in developing mathematical and scientific software bridging mathematics and interdisciplinary areas so that mathematics can be more accessible.

Research

My research is about answering the question: when can the qualitative properties of a parametrized system be described solely in terms of the parameters? In my PhD dissertation I tackled the eigenvalue configuration problem: given two parametric real symmetric matrices and a desired arrangement of their eigenvalues, produce a condition on the parameters so that the eigenvalues are arranged in a given way. This problem generalizes Descartes’ rule of signs.

Drag the points. The red points are the eigenvalues of a matrix F, the blue points are the eigenvalues of a matrix G, and the eigenvalue configuration counts how many blue points fall in each region marked under the line.

EC(F, G) =

For more information, see the Research page.

Education

  • North Carolina State University Ph.D Mathematics (2026)
  • Georgia Institute of Technology B.S. Mathematics, B.S. Computer Science (2021)

Work Experience

  • Naval Information Warfare Center (NIWC) Atlantic High Performance Computing Intern (Summer 2026)
    • AI/Machine Learning Workflows: Researched and developed an LLM workflow allowing users to create and interact with knowledge graphs using natural language. Utilized tools including Neo4J, Model-Context Protocol (MCP), and Retrieval-Augmented Generation (RAG).
    • High-Performance Scalable Data Pipelines: Engineered scalable data pipelines and automated machine learning workflows using Apache Spark, SQL, and Python to model maritime time-series data on high-performance computing clusters. Designed and evaluated complex data processing frameworks by implementing a genetic algorithm to construct graphical models from large-scale GPS datasets; executed statistical analysis to quantify model fit and performance.
  • Georgia Tech Research Institute (GTRI) Software Engineering Co-op (2018-2020)
    • Embedded Software Development: Practiced Agile methodologies to write clean, efficient, and maintainable code in Python, C#, and C++; authored comprehensive technical documentation.
    • Radar Systems: Designed, implemented, and maintained both backend and frontend features for radar systems testing software.

Talks

Publications

  1. Hong, Hoon, Daniel Profili, and J. Rafael Sendra. “Conditions for eigenvalue configurations of two real symmetric matrices (signature approach).”. SIAM Journal on Matrix Analysis and Applications (pending). (2026).
  2. Hong, Hoon, Daniel Profili, and J. Rafael Sendra. “Conditions for eigenvalue configurations of two real symmetric matrices (symmetric polynomials approach).” Journal of Symbolic Computation (pending) (2026).
  3. Santiesteban, Daniela Y., Diego S. Dumani, Daniel Profili, and Stanislav Y. Emelianov. Copper Sulfide Perfluorocarbon Nanodroplets as Clinically Relevant Photoacoustic/Ultrasound Imaging Agents. Nano Letters 2017 17 (10), 5984-5989, DOI: 10.1021/acs.nanolett.7b02105.