BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Umberto Hryniewicz (Aachen University)
DTSTART:20210727T160000Z
DTEND:20210727T170000Z
DTSTAMP:20260423T022622Z
UID:Geolis/54
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Geolis/54/">
 Contact three-manifolds with exactly two simple Reeb orbits</a>\nby Umbert
 o Hryniewicz (Aachen University) as part of Geometria em Lisboa (IST)\n\n\
 nAbstract\nThe goal of this talk is to present a complete characterization
  of Reeb flows on closed 3-manifolds with precisely two periodic orbits. T
 he main step consists in showing that a contact form with exactly two peri
 odic Reeb orbits is non-degenerate. The proof combines the ECH volume form
 ula with a study of the behavior of the ECH index under non-degenerate per
 turbations of the contact form. As a consequence\, the ambient contact 3-m
 anifold is a standard lens space\, the contact form is dynamically convex\
 , the Reeb flow admits a rational disk-like global surface of section and 
 the dynamics are described by a pseudorotation of the 2-disk. Moreover\, t
 he periods and rotation numbers of the closed orbits satisfy the same rela
 tions as (quotients of) irrational ellipsoids\, and in the case of S^3 the
  transverse knot-type of the periodic orbits is determined. Joint work wit
 h Cristofaro-Gardiner\, Hutchings and Liu.\n
LOCATION:https://researchseminars.org/talk/Geolis/54/
END:VEVENT
END:VCALENDAR