For a particular result in analysis with a snappy non-standard proof, there's this proof of the Bieri-Groves Theorem on tropical amoebas. (Does this count as "analysis"? I'm not sure.)
There are some nice applications of model theory to [differential Galois theory],2 partly due to the fact that the complete theory of differentially closed fields of characteristic zero happens to have extremely nice model theoretic properties (it's omega-stable, hence there nice rank functions on definable sets and unique-up-to-isomorphism prime models over any set of parameters).
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For a particular result in analysis with a snappy non-standard proof, there's this proof of the Bieri-Groves Theorem on tropical amoebas. (Does this count as "analysis"? I'm not sure.) |
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