On the work of Igor Frenkel
Bibliographic record
Abstract
Igor Frenkel is one of the leading representation theorists and mathematical physicists of our time. Inspired by the mathematical philosophy of Herman Weyl, who recognized the central role of representation theory in mathematics and its relevance to quantum physics, Frenkel made a number of foundational contributions at the juncture of these fields. A quintessential mathematical visionary and romantic, he has rarely followed the present day fashion. Instead, he has striven to get ahead of time and get a glimpse into the mathematics of the future – at least a decade, no less. In this, he has followed the example of I. M. Gelfand, whose approach to mathematics has always inspired him. He would often write several foundational papers in a subject, and then leave it for the future generations to be developed further. His ideas have sometimes been so bold and ambitious and so much ahead of their time that they would not be fully appreciated even by his students at the time of their formulation, and would produce a storm of activity only a few years later. And, of course, as a result, many of his ideas are still waiting for their time to go off. This text is a modest attempt by Igor’s students and colleagues of various generations to review his work, and to highlight how it has influenced in each case the development of the corresponding field in subsequent years.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.004 | 0.006 |
| Scholarly communication | 0.004 | 0.005 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.010 | 0.006 |
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".