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SUMMARY:Maksim Stokic (Tel Aviv University)
DTSTART:20221221T121000Z
DTEND:20221221T133000Z
DTSTAMP:20260423T024535Z
UID:GDS/71
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GDS/71/">Fle
 xibility of the adjoint action of the group of Hamiltonian diffeomorphisms
 </a>\nby Maksim Stokic (Tel Aviv University) as part of Geometry and Dynam
 ics seminar\n\n\nAbstract\nThe space of Hamiltonian diffeomorphisms has a 
 structure of an infinite \ndimensional Frechet Lie group\, with Lie algebr
 a isomorphic to the space \nof normalized functions and adjoint action giv
 en by pull-backs. We show \nthat this action is flexible: for a non-zero n
 ormalized function $f$\, \nany other normalized function can be written as
  a sum of differences of \nelements in the orbit of $f$ generated by the a
 djoint action. Additionally\, \nthe number of elements in this sum is domi
 nated from above by the \n$L_{\\infty}$-norm of $f$. This result can be in
 terpreted as an (bounded) \ninfinitesimal version of the Banyaga's result 
 on simplicity of $Ham(M\,\\omega)$. \nMoreover\, it can be used to remove 
 the $C^{\\infty}$-continuity condition \nin the Buhovsky-Ostrover theorem 
 on the uniqueness of Hofer's metric. \nThis is joint work with Lev Buhovsk
 y.\n
LOCATION:https://researchseminars.org/talk/GDS/71/
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