Positivity of Chern Classes of Symmetric Powers
The total Chern class of as a torus representation is a symmetric polynomial whose coefficients were conjectured positive, with a binomial log-concavity refinement. Both are established.
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Argument
- Field
- Enumerative geometry
- Posed by
- classical enumerative geometry
- Year posed
- —
- Years open
- —
- Solved
- 2026-05-24
- Model
- AlphaEvolve, ChatGPT 5.5 Pro
- Vendor
- Google DeepMind / OpenAI
- Collaborators
- Gergely Berczi, Laszlo M. Feher
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 15 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The paper calls itself a case study in synchronized AI-assisted mathematics and separates the two roles: AlphaEvolve served first as a searching engine and later as what the authors call a detective for structural recurrences, including a section-long account of one conjecture; ChatGPT 5.5 Pro acted as an interactive assistant for symbolic derivations.
Verification
arXiv preprint; not yet peer-reviewed.