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SUMMARY:Sobhan Seyfaddini (Institut de Mathématiques de Jussieu - Paris R
 ive Gauche)
DTSTART:20221129T160000Z
DTEND:20221129T170000Z
DTSTAMP:20260423T022732Z
UID:Geolis/104
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Geolis/104/"
 >On the algebraic structure of groups of area-preserving homeomorphisms</a
 >\nby Sobhan Seyfaddini (Institut de Mathématiques de Jussieu - Paris Riv
 e Gauche) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nIn an influe
 ntial article from the 1970s\, Albert Fathi\, having proven that the group
  of compactly supported volume-preserving homeomorphisms of the $n$-ball i
 s simple for $n\\geq 3$\, asked if the same statement holds in dimension $
 2$. In a joint work with Cristofaro-Gardiner and Humilière\, we proved th
 at 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.\n\nIn fact\, Fath
 i posed a more general question about all compact surfaces: is the group o
 f "Hamiltonian homeomorphisms" (which I will define) simple? In my talk\, 
 I will review recent joint work with Cristofaro-Gardiner\, Humilière\, Ma
 k and Smith answering this more general question of Fathi. The talk will b
 e for the most part elementary and will only briefly touch on Floer homolo
 gy which is a crucial ingredient of the solution.\n
LOCATION:https://researchseminars.org/talk/Geolis/104/
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