Logarchéon / Work Algorithms / Geometry

Shing-Tung Yau's Work Algorithms
Geometric Analysis, Calabi-Yau Geometry, and the Global PDE Method

This page reconstructs the working methods of Shing-Tung Yau (丘成桐; also approximated in some romanizations as Chin-Tong/Cheng-Tong Yau) from a 300-case bibliographic corpus. Each paper, book chapter, edited-volume contribution, survey, or lecture-like exposition is treated as a single “case”: a thesis, a result-type, and a set of overlapping methodological strategies.

The reconstruction is not a reproduction of copyrighted papers. It is a derived decision-tree model: titles and bibliographic families are used as the source spine, while the thesis/result summaries and strategy assignments are interpretive.

300 cases33 overlapping strategiescase-prevalence histogramsgeometric analysis / Calabi-Yau / GR / mirror symmetry
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Research Reconstruction

Yau's corpus repeatedly converts geometry into analysis and then back into geometry. The central pattern is: identify a geometric obstruction, encode it in nonlinear PDE, prove an a priori estimate ladder, and extract topology, canonical metrics, rigidity, or physical meaning. The same template appears in Calabi's conjecture, positive mass, harmonic maps, heat kernel estimates, Hermitian-Yang-Mills theory, mirror symmetry, graph geometry, and later mathematical-physics programs.

The histogram below is deliberately not normalized to sum to 100%. Strategies overlap. A single case may use three or four methods; therefore the correct statistic is prevalence per 300 cases.

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33-Strategy Decision Tree

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Overlapping Strategy Prevalence

Bar width = cases using strategy / 300. Percentages may add above 100% because strategies are not mutually exclusive.

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300 Paper / Chapter / Lecture Cases

IDYearSourceCase / Lecture TitleThesis / ResultStrategies
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Bibliographic Source Spine

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Worked Demonstrations

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Methodological Caution

This project reconstructs possible work algorithms from public bibliography and mathematical content families. It should not be read as a psychological claim about private cognition. The output is a probability-style ensemble over public work-products: what strategies best explain how a theorem, survey, or chapter is organized.