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Finitary and Infinitary Mathematics, Regularity and the Crossover Between Combinatorics and Analysis

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Part of the TMS Symposium

Szemeredi’s regularity lemma is a powerful tool in combinatorics, and has been described as a “structure theorem for graphs”. Both the statement and the proof can seem rather unenlightening—unless you see the analogy with some very well-known results in analysis and probability. More precisely, regularity is what you get when you take the proofs of these results and accidentally try to run them in a finite world.

I’ll try to present this picture while finding time to say what regularity is good for, and maybe touch on the machinery of compactness and ultrafilters that does all this stuff for you.

This talk is part of the Trinity Mathematical Society series.

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