PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Yakov Pesin.

Title:From discrete integrable systems to cluster algebras and back
Seminar:Department of Mathematics Colloquium
Speaker:Michael Gekthman, University of Notre Dame
Abstract Link:
The pentagram map that associates to a projective polygon a new one formed by intersections of short diagonals was introduced by R. Schwartz and was shown to be integrable by V. Ovsienko, R. Schwartz and S. Tabachnikov. Recently, M. Glick demonstrated that the pentagram map can be put into the framework of the theory of cluster algebras, a new and rapidly developing area with many exciting connections to diverse fields of mathematics. In this talk I will explain that, in fact, discrete integrable systems that can be viewed as generalizations of the pentagram map are intrinsic to a certain class of cluster algebras that are related to weighted directed networks on a torus and a cylinder. After presenting necessary background information on Poisson geometry of cluster algebras, I will show how all ingredients necessary for integrability - Poisson brackets, integrals of motion - can be recovered from combinatorics of a network. I will conclude with a geometric interpretation of discrete systems obtained through this approach.

Room Reservation Information

Room Number:MB114
Date:09 / 29 / 2011
Time:04:00pm - 05:00pm