Why Stability Matters: Interrelations between geom/discrete math/HEP/logic

NOTICES

Model Theory and Geometry

Mathematizing Kant's Transcendental Category

- A disciple of Saunders MacLane - Michael Morley: Categoricity in Power (He later joined Tarski school at UCB, under Vaught)
- From Loewenheim-Skolem, you cannot determine cardinality of infinite domain, but you can say categoricity under given cardinality
- Stability of categoricity: Saharon Shelah's efforts
- In the same period of Morley's above work, MacLane-Eilenberg theory of natural transformations turned into "category theory"
- William Lawvere, who related Quantifies and Shearves, was a disciple of Samuel Eilenberg, had "workshop" of mathematical logic at UCB Tarski school

Variational Principle and its relations to disciplines other than analysis

- PDE, Calculus of Variations in the Large, Harmonic Analysis
- giving global picture of Any potential distributions: which require infinite dimensions (non-zero energy in infrared), or, so to say, quantum dynamics
- At least two millennium problems are related: Yang-Mills and Navier-Stokes
- elliptization of parabolic PDE into infinte system of ODEs
- soliton characterization by Fermi-Pasta-Ulam and Zabusky-Kruskal
- Faddeev-Popov ghost
- In game theory, translation of n-person non-zerosum game to n+1-person zerosum game (extra player, like "natural resource", behave irrationally): In TGEB, von Neumann-Moregenstern gave a suggestion about relation to Morse theory
- In economics, explaining demands in classical general equilibrium with term structure of finance/dynamic macroeconomics

Conservation and Stability

- Stability in Model Theory
- which means degree of "power division" of time (real time)
- imaginary time, with conformal invariance, is algebraically determined, but no determinacy with real time: related to validity of path integral
- residue of energy, in order of log(t) and not absorbable to power structure (orbit), plays main role in non-linear phenomena
- In engineering, metrics in shorter time make precise control possible and which make systems more stable
- commensurability of orbits in planetary system
- ergodic theory
- basis of fourier analysis
- lattice structure of natural number >0 represented in product of primes (Dedekind)
- stability of economic equilibrium

Kakutani's contribution to understanding of stability

- I'm asking Shizuo Kakutani's significance to Princeton guys in 1940s
- origin of Kakutani's FPT and metamathematical counterpart of it

So What?