Curtis T. McMullen’s Work Algorithms

A deep 300-case reconstruction of McMullen’s method across complex dynamics, quasiconformal surgery, renormalization, Teichmüller theory, hyperbolic 3-manifolds, Kleinian groups, K3 surfaces, Salem numbers, billiards, translation surfaces, Hilbert modular surfaces, triangle groups, and moduli-space dynamics. Each case is treated as a methodological lecture: object, deformation language, invariant, computation, transfer principle, and theorem form.

33 Deep Strategies300 CasesDynamics · Teichmüller · 3-Manifolds · BilliardsMathJax-Safe Formula Rendering
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Reconstruction method

This is a bibliographic and methodological reconstruction, not a reproduction of McMullen’s papers, books, programs, notes, or unpublished materials. The source spine follows his public Harvard pages, official publication list, vita, book-level works, and course-note families. Strategy tags overlap: percentages are method-frequency indicators, not a probability distribution.

33strategies
300case lectures
12case families
900strategy tags

Core thesis

McMullen’s method repeatedly converts a difficult object into the neighboring geometry where its invariant is measurable: an algorithm becomes a rational map, a surface map becomes a hyperbolic 3-manifold, a billiard becomes a translation surface, and entropy becomes a spectral or arithmetic datum.

Deep reading unit

Each case is read as a pipeline: object → correct language → deformation or flow → invariant → table/example → cross-domain transfer → rigidity, classification, construction, or universality statement.

Why this style

The Conway/Galileo/Knuth/Connes template makes method visible: cards expose strategy; formulas expose compression; ranking exposes prevalence; corpus rows expose evidence; demonstrations expose how to apply the method.

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The McMullen strategy engine

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Overlapping prevalence ranking

Bars show count divided by 300 cases. Since a case carries multiple strategy tags, the displayed prevalence is a method-frequency map rather than a probability distribution.

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Decision tree for reading McMullen as method

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300-case corpus

#CaseFamilyDeep reading moveStrategies
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Source spine as control system

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Worked demonstrations