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BEGIN:VEVENT
UID:156c0205f136e071af4da96b362bbf59
CATEGORIES:Discrete Math
CREATED:20220303T111152
SUMMARY:Triangular-Grid Billiards and Plabic Graphs
LOCATION:Hill Center Room 705
DESCRIPTION:Abstract: Given a polygon P in the triangular grid, we define a rigid billi
 ards system by allowing beams of light to bounce around inside of P so that
  each beam always meets the midpoint of a unit-length boundary segment at a
  60-degree angle. This basic setup seems ripe for investigation; we will fo
 cus on some natural extremal questions concerning how large P must be relat
 ive to the number c of light-beam trajectories. Our main theorem states tha
 t the (appropriately normalized) area of P is at least 6c-6 and that the (a
 ppropriately normalized) perimeter of P is at least (7c-3)/2. This talk wil
 l sketch some of the geometric aspects of the proof of this result. We will
  also briefly discuss how one can reformulate these inequalities in the lan
 guage of Postnikov's plabic graphs. This talk is based on joint work with P
 akawut Jiradilok. \n
X-ALT-DESC;FMTTYPE=text/html:<p style="margin: 9pt 0in 0.0001pt;"><strong>Abstract</strong>: Given a pol
 ygon P in the triangular grid, we define a rigid billiards system by allowi
 ng beams of light to bounce around inside of P so that each beam always mee
 ts the midpoint of a unit-length boundary segment at a 60-degree angle. Thi
 s basic setup seems ripe for investigation; we will focus on some natural e
 xtremal questions concerning how large P must be relative to the number c o
 f light-beam trajectories. Our main theorem states that the (appropriately 
 normalized) area of P is at least 6c-6 and that the (appropriately normaliz
 ed) perimeter of P is at least (7c-3)/2. This talk will sketch some of the 
 geometric aspects of the proof of this result. We will also briefly discuss
  how one can reformulate these inequalities in the language of Postnikov's 
 plabic graphs. This talk is based on joint work with Pakawut Jiradilok.&nbs
 p;</p>
CONTACT:: Colin Defant (Princeton)
DTSTAMP:20260826T215139
DTSTART;TZID=America/New_York:20220307T140000
DTEND;TZID=America/New_York:20220307T150000
SEQUENCE:0
TRANSP:OPAQUE
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