BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Thomas Ivey (College of Charleston) DTSTART:20201214T160000Z DTEND:20201214T170000Z DTSTAMP:20260423T021227Z UID:DGSTO/7 DESCRIPTION:Title: Ne w Integrable Curve Flows in the Pseudoconformal 3-Sphere\nby Thomas Iv ey (College of Charleston) as part of Differential Geometry Seminar Torino \n\n\nAbstract\nThe pseudoconformal 3-sphere $S^3$ is the projectivization of the null cone in $\\mathbb C^3$ with the standard pseudo-Hermitian inn er product. The Lie group $SU(2\,1)$ fixing this metric naturally acts on the sphere\, preserving a contact structure\, and can be identified with t he pseudoconformal frame bundle of $S^3$. By normalizing lifts to the fram e bundle\, we define scalar geometric invariants for Legendrian curves (L- curves) in $S^3$\, and for curves transverse to the contact planes (T-curv es).\nWe seek invariant geometric flows for these parametrized curves that induce integrable evolution systems for the invariants. While there is an infinite sequence of geometric flows for L-curves inducing the Boussinesq hierarchy\, for T-curves there is another infinite sequence of flows that induces a sequence of 3-component evolution systems for the invariants\, evidently a novel integrable bi-Hamiltonian hierarchy. This closely resem bles the NLS hierarchy\, itself realized by a sequence of curve flows in E uclidean 3-space\, including the vortex filament equation. We discuss som e common features of these hierarchies\, describe the geometry and dynamic s of travelling wave solutions (also arising as critical curves for Lagran gians derived from the conserved densities) and conclude with some open qu estions.\n LOCATION:https://researchseminars.org/talk/DGSTO/7/ END:VEVENT END:VCALENDAR