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PRODID:-//Memento EPFL//
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SUMMARY:Complexity of almost-toric integrable Hamiltonian systems
DTSTART:20140225T161500
DTEND:20140225T170000
DTSTAMP:20261005T001416Z
UID:8086fc048312b3a84745c0f2519e1b53607e10a993400479b284b311
CATEGORIES:Conferences - Seminars
DESCRIPTION:Christophe Wacheux (EPFL)\nGeometry and Dynamics Seminar\nAbst
 ract: In this talk I will discuss integrable Hamiltonian systems on symple
 ctic manifolds. First\, I recall the results existing near regular points.
  Later I will focus on the study of non-degenerate critical points and exp
 lain why the transition from them to non-degenrate critical singularities 
 needs a study of their own.\nFirst\, the toric systems\, that is\, integra
 ble Hamiltonian systems whose components of the moment map are periodic. T
 his amounts to the description of elliptic singularities with Atiyah - Gui
 llemin & Sternberg theorem\, and Delzant classification by moment polytope
 s.\nNext\, the almost-toric systems\, that is\, integrable Hamiltonian sys
 tems whose n-c last components of the moment map are all periodics. We kee
 p the terminology "semi-toric systems" for the case c=1\, which is more si
 mple. Study of almost and semi-toric systems is a subject on its own\, but
  today\, we shall focus on the almost-toric case.\nThat is why I will intr
 oduce the Williamson indices (k_e\,k_f\,k_h\,k_x) and describe the structu
 re of poset they carry. Lastly\, I finish defining the complexity c\, and 
 explain its links to all the notions that we have introduced.
LOCATION:MA A3 31 http://plan.epfl.ch/?room=MA%20A3%2031
STATUS:CONFIRMED
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