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SUMMARY:Leonardo Macarini (IMPA)
DTSTART:20260529T130000Z
DTEND:20260529T143000Z
DTSTAMP:20260604T125137Z
UID:SissaAnalysisSeminar/16
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SissaAnalysi
 sSeminar/16/">Multiplicity of closed Reeb orbits on contact manifolds with
  periodic equivariant symplectic homology</a>\nby Leonardo Macarini (IMPA)
  as part of SISSA's Analysis seminars\n\nLecture held in 133.\n\nAbstract\
 nWe consider closed contact manifolds $(M\,\\xi)$ with periodic positive e
 quivariant symplectic homology. This is a very large class of contact mani
 folds and\, to the best of our knowledge\, includes all currently known ex
 amples admitting Reeb flows with finitely many closed orbits for which equ
 ivariant symplectic homology is a well defined invariant. Under weak index
  assumptions on a non-degenerate contact form $\\alpha$ on $M$\, we establ
 ish a sharp lower bound $r_M$ for the number of closed Reeb orbits of $\\a
 lpha$\, and show that equality holds if and only if $\\alpha$ is lacunary.
  The bound $r_M$ is essentially determined by the deviation of a suitable 
 finite sum of the contact Betti numbers of $M$ from its asymptotic average
 . We also compute $r_M$ for a broad class of examples\, including several 
 prequantizations of symplectic orbifolds\, and show that in this case $r_M
 =\\dim \\H_*(M/S^1\;\\Q)$. This is joint work with Miguel Abreu.\n
LOCATION:https://researchseminars.org/talk/SissaAnalysisSeminar/16/
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