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DTSTART;TZID=America/New_York:20241101T130000
DTEND;TZID=America/New_York:20241101T135000
DTSTAMP:20241114T084852
CREATED:20241101T170000Z
LAST-MODIFIED:20241030T145049Z
UID:153006-1730466000-1730469000@events.williams.edu
SUMMARY:Hopf's Theorem for Magnetic Systems Without Conjugate Points by Ivo Terek\, Williams College
DESCRIPTION:Hopf’s Theorem for Magnetic Systems Without Conjugate Points by Ivo Terek\, Williams College\, Friday November 1\, 1:00 – 1:50pm\, North Science Building 015\, Wachenheim\, Faculty Seminar \n \nAbstract: A magnetic system is the mathematical model used to study the trajectories of particles in a Riemannian manifold under the action of a magnetic field. Namely\, such trajectories are described as solutions of the Landau-Hall equation (a non-homogeneous version of the classical geodesic equation). The flow induced by the Landau-Hall equation in the tangent bundle is Hamiltonian and leaves all s-sphere bundles invariant\, with its dynamical behavior strongly depending on the value of s. We review basic facts about magnetic systems\, as well as the notion of magnetic curvature recently introduced by Assenza\, and use tools from Riemannian geometry to extend E. Hopf’s theorem — “no conjugate points implies non-positive total scalar curvature” — to the setting of magnetic systems. This is joint work with Valerio Assenza and James Marshall Reber. \n
URL:https://events.williams.edu/event/hopfs-theorem-for-magnetic-systems-without-conjugate-points-by-ivo-terek-williams-college/
LOCATION:Wachenheim Science Center\, Williamstown\, MA\, 01267\, United States
CATEGORIES:Event
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