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CATEGORIES:Trinity Mathematical Society
SUMMARY:Elliptical billiards and Poncelet trajectories - P
rofessor Pelham Wilson (DPMMS)
DTSTART;TZID=Europe/London:20190304T203000
DTEND;TZID=Europe/London:20190304T213000
UID:TALK118270AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/118270
DESCRIPTION:Given an elliptical billiard table\, to any ball t
rajectory which doesn't cross the line segment joi
ning the two foci\, there is an associated smaller
confocal ellipse inscribed in the trajectory. A P
oncelet trajectory is one which is closed after a
finite number of bounces. We'll see that if there
is one such closed trajectory with n segments\, th
en starting from every point on the outer ellipse\
, there is a similar closed trajectory with n segm
ents and the same inscribed ellipse\, and indeed a
ll these trajectories have the same length\n An
alogous geometric properties hold more generally f
or any pair of conics in the plane\, and in modern
terminology the existence of analogous Poncelet p
olygons is related to the torsion points on an ass
ociated elliptic curve.
LOCATION:Winstanley Lecture Theatre\, Trinity College
CONTACT:
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