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On singularity confinement for the pentagram map October 08, 2012 (02:10 PM PDT - 03:00 PM PDT)
Parent Program: --
Location: UC Berkeley
Speaker(s) Max Glick (Ohio State University)
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The UC Berkeley Combinatorics Seminar
Mondays 2:10pm - 3:00pm
939 Evans Hall
Organizers: Florian Block, Max Glick, and Lauren Williams

On singularity confinement for the pentagram map
Speaker: Max Glick

The pentagram map, introduced by R. Schwartz, is a birational map on the configuration space of polygons in the projective plane. We study the singularities of the iterates of the pentagram map. We show that a typical singularity disappears after a finite number of iterations, a confinement phenomenon first discovered by Schwartz. We provide a method to bypass such a singular patch by directly constructing the first subsequent iterate that is well defined on the singular locus under consideration. The key ingredient of this construction is the notion of a decorated (twisted) polygon, and the extension of the pentagram map to the corresponding decorated configuration space.

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