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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:<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:20260826T204157
DTSTART;TZID=America/New_York:20220307T140000
DTEND;TZID=America/New_York:20220307T150000
SEQUENCE:0
TRANSP:OPAQUE
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