BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Luca Asselle (Ruhr University Bochum) DTSTART:20211019T153000Z DTEND:20211019T163000Z DTSTAMP:20260423T022725Z UID:Geolis/62 DESCRIPTION:Title: A Morse complex for the Hamiltonian action in cotangent bundles\nby Lu ca Asselle (Ruhr University Bochum) as part of Geometria em Lisboa (IST)\n \n\nAbstract\nCritical points having infinite Morse index and co-index are invisible to homotopy theory\, since attaching an infinite dimensional ce ll does not produce any change in the topology of sublevel sets. Therefore \, no classical Morse theory can possibly exist for strongly indefinite fu nctionals (i.e. functionals whose all critical points have infinite Morse index and co-index). In this talk\, we will briefly explain how to instead construct a Morse complex for certain classes of strongly indefinite func tionals on a Hilbert manifold by looking at the intersection between stabl e and unstable manifolds of critical points whose difference of (suitably defined) relative indices is one. As a concrete example\, we will consider the case of the Hamiltonian action functional defined by a smooth time-pe riodic Hamiltonian $H: S^1 \\times T^*Q \\to \\mathbb R$\, where $T^*Q$ is the cotangent bundle of a closed manifold $Q$. As one expects\, in this c ase the resulting Morse homology is isomorphic to the Floer homology of $T ^*Q$\, however the Morse complex approach has several advantages over Floe r homology which will be discussed if time permits. This is joint work wit h Alberto Abbondandolo and Maciej Starostka.\n LOCATION:https://researchseminars.org/talk/Geolis/62/ END:VEVENT END:VCALENDAR