Seminar

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.