Deformations and Contractions in Mathematics and Physics
Bibliographic record
Abstract
Deformations of mathematical structures are not only important in most parts of mathematics but also to a large extend in physics. Contractions are in some respect dual to deformations. The aim of the proposed workshop was to bring together world experts in these complementary topics of deformations and contractions of various algebraic structures. Deformations and contractions have been investigated by researchers who had different approaches and goals. Tools such as cohomology, gradings, etc. which are utilized in the study of one concept, are likely to be useful for the other concept as well. At this meeting there were mathematicians, mathematical physicists and physicists as well. The organizers hope that the meeting was of benefit to all groups. Because various fields in mathematics and physics exist in which deformations are used, it was necessary to focus the topic of the workshop. The meeting mainly considered deformations of algebras (in particular, of Lie algebras), groups, and related algebraic structures, the corresponding contractions, and their applications to problems in physics. Nevertheless, other fields with strong relations to the central topic were present too. One such field, discussed in detail at the workshop, with tight interaction was deformation quantization. But also other topics like quantum groups, deformation of Hopf algebras, q-deformed physics, fuzzy spaces, quantum systems as deformations of classical systems, etc showed up. As the workshop had an interdisciplinary character it was considered to be useful to start with some introductory talks on with the aim to introduce the necessary concepts which were not always well known to all the different communities present. For more details on the concepts, see the corresponding extended abstracts in this Oberwolfach report. The following is a (non-exhaustive) list of topics which were discussed at the workshop. The workshop was attended by 44 participants from all over the world. The official program consisted of 24 lectures. Two evening sessions of informal presentations were organised. Beside the official program, there was ample time for the participants for further activities, such as self-organised sessions and discussion groups.
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 | 0.002 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.011 |
| Scholarly communication | 0.004 | 0.009 |
| Open science | 0.001 | 0.004 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.008 | 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".