BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Annalisa Calini (Charleston University) DTSTART:20200922T144500Z DTEND:20200922T160000Z DTSTAMP:20260404T120127Z UID:GDMSeminar/9 DESCRIPTION:Title: Geometric flows in centro-affine space\nby Annalisa Calini (Charles ton University) as part of Geometry\, Dynamics and Mechanics Seminar\n\n\n Abstract\nMany classical objects in differential geometry are described by integrable systems: nonlinear PDE with infinitely many conserved quantit ies that are (in some sense) solvable. Beginning in the 1980s\, studies of curve evolutions that are invariant under the action of a geometric group of transformations have unveiled more connections between geometric curve flows and well-known integrable PDE (among them are the KdV\, mKdV\, sin e-Gordon\, and NLS equations). More recently\, efforts have been directed towards understanding geometric discretizations of surfaces and curves an d associated evolutions.\nThis talk will describe some natural geometric flows for curves and polygons in centro-affine geometry\, and their relat ions with the KdV and Boussinesq equations and discretizations of Adler-Ge l’fand-Dikii (AGD) flows for curves in projective space. The AGD discre tizations (previously introduced in work by Marí-Beffa and Wang) will be discussed in more detail\, as their lifts to the moduli space of centro-a ffine arc length parametrized polygons promptly reveal their bihamiltonian structures in terms of a pair of simple pre-symplectic forms.\n\nSome ref erences:\n\nU. Pinkall\, Hamiltonian flows on the space of star-shaped cur ves\, Result. Math. 27 (1995)\, 328–332.\n\nA. Calini\, T. Ivey\, and G. Marí-Beffa\, Remarks on KdV-type Flows on Star-Shaped Curves\, Physica D Vol. 238\, no. 8 (2009)\, 788–797\n\nG. Marí-Beffa and J.P. Wang\, Ham iltonian structures and integrable evolutions of twisted gons in RPn\, Non linearity 26 (2013) 2515-2551\n\nA. Calini\, T. Ivey\, and G. Marí-Beffa\ , An integrable flow for starlike curves in centroaffine space\, SIGMA 9 \, (2013)\, 022\, 21 pp.\n\nA. Calini and G. Marí-Beffa\, Integrable evol utions of twisted polygons in centroaffine Rm\, IMRN\, rnaa161 (2020)\n LOCATION:https://researchseminars.org/talk/GDMSeminar/9/ END:VEVENT END:VCALENDAR