Michael R. Zeng 曽若凡 Graduate student in mathematics

Research

Spanning lines
A spanning line configuration, made with vZome.

Research Interests

I am interested in Schubert calculus, intersection theory on moduli stacks, and enumerative geometry. I am also interested in using machine learning and artificial intelligence to facilitate mathematical discoveries.

Some of the things I like to think about recently include lines on quartic surfaces, the $K_0$-ring of some moduli stacks, nef divisors on $\overline{\mathscr{M}}_{g,n}$, line bundles of toric varieties, and moduli of stable maps.

Publications & Preprints

Pure Mathematics

  1. Oriented Cohomology Rings of Some Moduli Spaces via Blowups, with Arkamouli Debnath. 2026. arXiv:2604.14536.
  2. The Grothendieck group of the variety of spanning line configurations. 2025. arXiv:2512.22769.
  3. $C_p$-Mackey Functors in Macaulay2, with Thomas Brazelton, David Chan, Benjamin Mudrak, Ben Spitz, Chase Vogeli, Chenglu Wang, and Sasha Zotine. 2025. Accepted by Journal of Software for Algebra and Geometry. arXiv:2509.05456.
  4. Brackets and Projective Geometry in Macaulay2, with Dalton Bidleman, Timothy Duff, and Jack Kendrick. 2025. arXiv:2504.00889.
  5. Appendix in: M. Harada and M. Precup, “Torus fixed point sets of Hessenberg Schubert varieties in regular semisimple Hessenberg varieties.” Osaka Journal of Mathematics 60 (2023), 637–652. arXiv:2112.13250.

AI for Mathematics

  1. Alternating Groups and Embeddings into Groups Invariably Generated by Two Prime-Order Elements, with Ting Gong and Yong Yang. 2026. arXiv:2608.00703.
  2. Albilich: Steerable Proof-State Orchestration for LLM-Based Mathematical Research with CAS Integration, with Ting Gong and Yong Yang. 2026. arXiv:2607.27705.
  3. FactorLibrary: From Polynomials to Circuits via Recursive Subgoals, with Rohan Pandey, Weikun K. Zhang, Kaijie Jin, Naomi Morato, Archit Ganapule, Bhaumik Mehta, and Jarod Alper. In 3rd AI for Math Workshop (ICML 2026): Toward Self-Evolving Scientific Agents. arXiv:2606.25394 · OpenReview.
  4. CircuitBuilder: From Polynomials to Circuits via Reinforcement Learning, with Weikun K. Zhang, Rohan Pandey, Bhaumik Mehta, Kaijie Jin, Naomi Morato, Archit Ganapule, and Jarod Alper. In ICLR 2026 Workshop on AI with Recursive Self-Improvement. arXiv:2603.17075.

AI for Languages

  1. Quantitative Orthographic Analysis of the Ogura Shikishi, with Paul S. Atkins. manuscript cultures 26.1 (2026), 1–60. doi:10.15460/s8e93666.
  2. Jibo-labeled classical hiragana image dataset, with Herman Chau and Paul S. Atkins. Zenodo, 2026. doi:10.5281/zenodo.18765466.
  3. Deriving Orthographic Data from Classical Japanese Texts with Machine-Learning Methods, with Herman Chau and Paul Atkins. In Proceedings of IPSJ SIG Computers and the Humanities, 2025. Jinmoncom 2025 Best Paper Award (じんもんこん2025 優秀論文賞) & Student Encouragement Award (学生奨励賞). URI: hdl.handle.net/1773/55355.