Derek R. Aoki

Interests

Pure mathematics and theoretical computer science, including algebraic geometry and topics related to logic (such as descriptive set theory and descriptive complexity theory). Recent mathematics courses include:

• Topology: linear topology; point set topology; Baire & Polish spaces
• Algebra: classical linear groups; noncommutative rings
• Analysis: functional analysis
• Computation & logic: computable structures, model-theoretic logics, forcing

Research(-adjacent) experience

• 2026. MIT PRIMES-USA. Research on Schubert calculus (texts: Lakshmibai & Brown).
• Summer 2025. Euler Circle Summer Course on Differential Geometry. Expository paper on diffeomorphism groups (texts: Mann, Banyaga).
• Spring 2025. Directed reading in finite model theory (texts: Libkin).
• Fall 2024. Independent side project on probabilistic computational complexity classes.
• Summer 2024. Euler Circle Summer Course on Independent Research & Proof Writing (IRPW). Expository paper on descriptive complexity theory (texts: Immerman).
• Spring 2024. Directed reading in descriptive set theory (texts: Kechris, Moschovakis).
• Summer 2023. NYU Ability Project. Maker work: CircuitPython, 3D printing, etc.
• 2022-2023. Project on AI literacy in early secondary education.

Publications

• D.R. Aoki (2026). About Infinite Algebraic Curves whose Indefinite Lengths Equal an Elliptic Arc: An English Translation of E780. Euleriana 6(1), pp.3-15. DOI:10.56031/2693-9908.1107
• A. Woodruff, A.S. Voneche, K. Thunstrom, R. Jana, R.L. Hardy, D.R. Aoki, P.G. Kelley (2023). “Discover AI in Daily Life”: An AI Literacy Lesson for Middle School Students. Proceedings of the 54th ACM Technical Symposium on Computer Science Education (SIGCSE), V.2, 1327. DOI:10.1145/3545947.3576224

Preprints

• D.R. Aoki (2026). On Open Borel Orbits in Conormal Bundles to Schubert Cells. arXiv:2610.35923
  • Oral presentation, 2026 MIT PRIMES Conference
  • Poster presentation, 2027 Joint Mathematical Meetings
• D.R. Aoki (2026). Order-Invariant CFO Contains Local-Order-Invariant FO.
• D.R. Aoki (2025). Local-Order-Invariant Logic on Classes of Bounded Degree. arXiv:2512.02039

Expository writing

• D.R. Aoki (2025). An Introduction to Diffeomorphism Groups.
  • D.R. Aoki (2025). Perfect Diffeomorphism Groups. Euler Circle Summer Course on Differential Geometry.
• D. Aoki (2024). On the Polynomial Hierarchy, PSPACE, and Descriptive Complexity. Euler Circle Summer Course on Independent Research & Proof Writing (IRPW).

Miscellany

• Erdős number = 4.
• Honorable Mention, 2023 AMS Math Poetry Contest.