Perverse schobers and 3d mirror symmetry
Bibliographic record
Abstract
The proposed physical duality known as 3d mirror symmetry relates the geometries of dual pairs of holomorphic symplectic stacks. It has served in recent years as a guiding principle for developments in representation theory. However, due to the lack of definitions, thus far only small pieces of the subject have been mathematically accessible. In this paper, we formulate abelian 3d mirror symmetry as an equivalence between a pair of 2-categories constructed from the algebraic and symplectic geometry, respectively, of Gale dual toric cotangent stacks. In the simplest case, our theorem provides a spectral description of the 2-category of spherical functors – i.e., perverse schobers on the affine line with singularities at the origin. We expect that our results can be extended from toric cotangent stacks to hypertoric varieties, which would provide a categorification of previous results on Koszul duality for hypertoric categories \mathcal{O} . Our methods also suggest approaches to 2-categorical 3d mirror symmetry for more general classes of spaces of interest in geometric representation theory. Along the way, we establish two results that may be of independent interest: (1) a version of the theory of Smith ideals in the setting of stable \infty -categories; and (2) an ambidexterity result for co/limits of presentable enriched \infty -categories over \infty -groupoids.
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 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.000 | 0.003 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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 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".