Structures quantiques de certaines sous-variétés lagrangiennes non-monotones
Bibliographic record
Abstract
Soit (M,ω) un variété symplectique fermée et connexe.On considère des sous-variétés\nlagrangiennes α : L → (M,ω). Si α est monotone, c.- à-d. s’il existe η > 0 tel que ημ = ω,\nPaul Biran et Octav Conea ont défini une version relative de l’homologie quantique. Dans ce contexte ils ont déformé l’opérateur de bord du complexe de\nMorse ainsi que le produit d’intersection à l’aide de disques pseudo-holomorphes. On\nnote (QH(L), ∗), l’homologie quantique de L munie du produit quantique.\nLe principal objectif de cette dissertation est de généraliser leur construction à un\nclasse plus large d’espaces. Plus précisément on considère soit des sous-variétés presque\nmonotone, c.-à-d. α est C1-proche d’un plongement lagrangian monotone ; soit les fibres\ntoriques de variétés toriques Fano. Dans ces cas non nécessairement monotones, QH(L)\nva dépendre de certains choix, mais cela sera irrelevant pour les applications présentées\nici.\nDans le cas presque monotone, on s’intéresse principalement à des questions de\ndéplaçabilité, d’uniréglage et d’estimation d’énergie de difféomorphismes hamiltoniens.\n\n\nEnfin nous terminons par une application combinant les deux approches, concernant\nla dynamique d’un hamiltonien déplaçant toutes les fibres toriques non-monotones dans\nCPn.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.010 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".