Mini-Workshop: New Developments in Newton-Okounkov Bodies
Bibliographic record
Abstract
The theory of Newton-Okounkov bodies, also called Okounkov bodies, is a new connection between algebraic geometry and convex geometry. It generalizes the well-known and extremely rich correspondence between geometry of toric varieties and combinatorics of convex integral polytopes. Okounkov bodies were first introduced by Andrei Okounkov, in a construction motivated by a question of Khovanskii concerning convex bodies govering the multiplicities of representations. Recently, Kaveh-Khovanskii and Lazarsfeld-Mustata have generalized and systematically developed Okounkov’s construction, showing the existence of convex bodies which capture much of the asymptotic information about the geometry of ( X,D ) where X is an algebraic variety and D is a big divisor. The study of Okounkov bodies is a new research area with many open questions. The goal of this mini-workshop was to bring together a core group of algebraic/symplectic geometers currently working on this topic to establish the groundwork for future development of this area.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".