Area-preserving transformations and symplectic geometry

Talk by Sobhan Seyfaddini, ETHZ

Abstract : In an influential article from the 1970s, Albert Fathi, having proven that the group of compactly supported volume-preserving homeomorphisms of the n-ball is simple for n ≥ 3, asked if the same statement holds in dimension 2. In a joint work with Cristofaro-Gardiner and Humiliére, we proved that the group of compactly supported area-preserving homeomorphisms of the 2-disc is not simple. This answers Fathi's question and settles what is known as the simplicity conjecture in the affirmative.  We will discuss Fathi’s problem and its solution.

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