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NCTS Differential Geometry Seminar
16:00 - 17:00, December 12, 2018 (Wednesday)
Room 440, Astronomy-Mathematics Building, NTU
(台灣大學天文數學館 440室)
Polygonal Billiards, Liouville Currents, and Rigidity
Christopher J. Leininger (University of Illinois at Urbana-Champaign)


A particle bouncing around inside a Euclidean polygon gives rise to a biinfinite "bounce sequence" (or "cutting sequence") recording the (labeled) sides encountered by the particle. In this talk, I will describe recent work with Duchin, Erlandsson, and Sadanand, in which we prove that the set of all bounce sequences -- the "bounce spectrum" -- essentially determines the shape of the polygon. This is consequence of our main result about Liouville currents on surfaces associated to nonpositively curved Euclidean cone metrics. In the talk I will explain the objects mentioned above, how they relate to each other, and give some idea of the proof of the main theorem.


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