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Geometric Analysis Seminar

A tale of forgetful electrons

Dan Ketover - Rutgers University

Location:  Hill 705
Date & time: Tuesday, 19 February 2019 at 3:00PM - 4:00PM

Abstract:  In the early 80s Vladimir Arnold asked whether every Riemannian two-sphere for each c>0 contains a closed immersed curve of curvature c.  Such curves are orbits of a charged particle subject to a magnetic field.  The problem is much more subtle than the case c=0 of geodesics and has been studied in symplectic geometry and dynamical systems.   I will explain joint work with Y. Liokumovich where we show the existence of weak solutions to Arnold’s conjecture.  Namely, I'll show that on any Riemannian surface (not necessarily a two-sphere) there always exists a C^{1,1} solution. 

Postponed from Feb. 12th