Root Bounds for Chain Polynomials Beyond the Cohen–Macaulay World
P. Dugan. "Root bounds for chain polynomials beyond the Cohen–Macaulay world." Preprint, 2026.
CV
Education
- University of Pennsylvania, Philadelphia, PA, expected December 2027
- M.S.E. in Computer Science (submatriculation), B.S.E. in Computer Science, B.A. in Mathematics
- GPA 4.0/4.0
- Current coursework: Theory of Machine Learning (Michael Kearns), Machine Perception
Research
- Real root bounds for chain and walk-generating polynomials (independent research, 2025–2026)
- Proved that a sign-alternation condition on (I + aA)⁻¹ for a weighted DAG confines all real roots of its walk-generating polynomials to [−a, 0].
- Consequences: a sharp [−4, 0] for the chain polynomial of every finite graded poset, [−4/(q+1), 0] for subspace lattices, and [−1/k, 0] for k-Eulerian posets. The proofs are elementary and avoid homological methods.
- Preprint submitted to the Electronic Journal of Combinatorics (PDF).
Experience
- Compiler / AI Engineering Intern, Concurrent EDA, Pittsburgh, PA (May–Aug 2026)
- Built an LLM-driven agent for end-to-end FPGA development (HDL generation → synthesis → optimization) on MLIR/LLVM with a custom MCP tool server.
- Wrote automated optimization passes, design-analysis heuristics, and code-rewrite tools for the agent.
- Compared with an unassisted LLM baseline: 16× fewer tokens, 30–40% faster design iteration, and synthesizable HDL up from 80% to 100%.
- Machine Learning Engineer, Palm Cosmetics, remote (2025–2026)
- Built a computer-vision pipeline that measures nail shape and size from customer video and classifies nail type for product sizing. It holds up under real-world lighting, camera angles, and hand positions.
- Data Science Intern, Carnegie Mellon University REUSE, Pittsburgh, PA (May–Aug 2025)
- Built data pipelines over large volumes of GitHub event data and NLP models to detect shifts in developer behavior in the Rust ecosystem, for faculty research on open-source collaboration.
Publications
Teaching
Projects
Skills
- Languages: Python, C, C++, Java, Haskell, OCaml, SQL, JavaScript/TypeScript, Bash
- ML: PyTorch, TensorFlow, scikit-learn, Hugging Face, NumPy, pandas; LLM agents, MCP, retrieval, computer vision
- Systems: LLVM, MLIR, FPGA/HDL toolchains, Docker, Spark, AWS, PostgreSQL, Git, Linux
- Mathematics: combinatorics, abstract algebra, spectral graph theory, learning theory (PAC, VC dimension), projective geometry, measure theory, functional analysis
- Spoken: English (native), Japanese (elementary)
Service and leadership
- Member, Penn Stwing