BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Rémi Leclercq (Université Paris-Saclay) DTSTART:20231219T160000Z DTEND:20231219T170000Z DTSTAMP:20260423T022740Z UID:Geolis/139 DESCRIPTION:Title: Essential loops of Hamiltonian homeomorphisms\nby Rémi Leclercq (Uni versité Paris-Saclay) as part of Geometria em Lisboa (IST)\n\n\nAbstract\ nIn 1987\, Gromov and Eliashberg showed that if a sequence of diffeomorphi sms preserving a symplectic form C⁰ converges to a diffeomorphism\, the limit also preserves the symplectic form -- even though this is a C¹ cond ition. This result gave rise to the notion of symplectic homeomorphisms\, i.e. elements of the C⁰-closure of the group of symplectomorphisms in th at of homeomorphisms\, and started the study of "continuous symplectic geo metry".\n\nIn this talk\, I will present recent progress in understanding the fundamental group of the C⁰-closure of the group of Hamiltonian diff eomorphisms in that of homeomorphisms. More precisely\, I will explain a s ufficient condition which ensures that certain essential loops of Hamilton ian diffeomorphisms remain essential when seen as "Hamiltonian homeomorphi sms". I will illustrate this method (and its limits) on toric manifolds\, namely complex projective spaces\, rational products of 2-spheres\, and ra tional 1-point blow-ups of CP².\n\nOur condition is based on (explicit) c omputation of the spectral norm of loops of Hamiltonian diffeomorphisms wh ich is of independent interest. For example\, in the case of 1-point blow- ups of CP²\, I will show that the spectral norm exhibits a surprising beh avior which heavily depends on the choice of the symplectic form. This is joint work with Vincent Humilière and Alexandre Jannaud.\n LOCATION:https://researchseminars.org/talk/Geolis/139/ END:VEVENT END:VCALENDAR