Von Neumann Algebras and Ergodic Theory of Group Actions
Why this work is in the frame
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Bibliographic record
Abstract
The workshop \emph{Von Neumann Algebras and Ergodic Theory of Group Actions} was organized by Dietmar Bisch (Vanderbilt University, Nashville), Damien Gaboriau (ENS Lyon), Vaughan Jones (UC Berkeley) and Sorin Popa (UC Los Angeles). It was held in Oberwolfach from October 26 to November 1, 2008. This workshop was the first Oberwolfach meeting on von Neumann algebras and orbit equivalence ergodic theory. The organizers took special care to invite many young mathematicians and more than half of the 28 talks were given by them. The meeting was very well attended by over 40 participants, leading senior researchers and junior mathematicians in the field alike. Participants came from about a dozen different countries including Belgium, Canada, Denmark, France, Germany, Great Britain, Japan, Poland, Switzerland and the USA. The first day of the workshop featured beautiful introductory talks to orbit equivalence and von Neumann algebras (Gaboriau), Popa's deformation/rigidity techniques and applications to rigidity in II _1 factors (Vaes), subfactors and planar algebras (Bisch), random matrices, free probability and subfactors (Shlyakhtenko), subfactor lattices and conformal field theory (Xu) and an open problem session (Popa). There were many excellent lectures during the subsequent days of the conference and many new results were presented, some for the first time during this meeting. A few of the highlights of the workshop were Vaes' report on a new cocycle superrigidity result for non-singular actions of lattices in SL(n, \mathbb R ) on {\mathbb R}^n and on other homogeneous spaces (joint with Popa), Ioana's result showing that every sub-equivalence relation of the equivalence relation arising from the standard SL(2, \mathbb Z )-action on the 2 -torus {\mathbb T}^2 is either hyperfinite, or has relative property (T), and Epstein's report on her result that every countable, non-amenable group admits continuum many non-orbit equivalent, free, measure preserving, ergodic actions on a standard probability space. Other talks discussed new results on fundamental groups of II _1 factors, L ^2 -rigidity in von Neumann algebras, II _1 factors with at most one Cartan subalgebra, subfactors from Hadamard matrices, a new construction of subfactors from a planar algebra and new results on topological rigidity and the Atiyah conjecture. Many interactions and stimulating discussions took place at this workshop, which is of course exactly what the organizers had intended. The organizers would like to thank the Mathematisches Forschungsinstitut Oberwolfach for providing the splendid environnment for holding this conference. Special thanks go to the very helpful and competent staff of the institute.
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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 | 0.001 | 0.001 |
| 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) | 0.000 | 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 it