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SUMMARY:Elliptical billiards and Poncelet trajectories - Professor Pelham 
 Wilson (DPMMS)
DTSTART:20190304T203000Z
DTEND:20190304T213000Z
UID:TALK118270@talks.cam.ac.uk
CONTACT:73969
DESCRIPTION:Given an elliptical billiard table\, to any ball trajectory wh
 ich doesn't cross the line segment joining the two foci\, there is an asso
 ciated smaller confocal ellipse inscribed in the trajectory. A Poncelet tr
 ajectory is one which is closed after a finite number of bounces. We'll se
 e that if there is one such closed trajectory with n segments\, then start
 ing from every point on the outer ellipse\, there is a similar closed traj
 ectory with n segments and the same inscribed ellipse\, and indeed all the
 se trajectories have the same length\n    Analogous geometric properties h
 old more generally for any pair of conics in the plane\, and in modern ter
 minology the existence of analogous Poncelet polygons is related to the to
 rsion points on an associated elliptic curve.
LOCATION:Winstanley Lecture Theatre\, Trinity College
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