|Date: Friday, February 27, 2015
Location: 3866 East Hall (4:10 PM to 5:00 PM)
Title: Integrable cluster dynamics of directed networks and pentagram maps
Abstract: The pentagram map was introduced by R. Schwartz more than 20 years ago. In 2009, V. Ovsienko, R. Schwartz and S. Tabachnikov established complete Liouville integrability of this discrete dynamical system. In 2011, M. Glick interpreted the pentagram map as a composition of cluster transformations associated with a special quiver. Using our previous results on cluster algebras and Poisson geometry of directed networks on surfaces, we generalize Glick's construction to include the pentagram map into a family of discrete integrable maps and to study their properties.
Joint work with M. Gekhtman, M. Shapiro and S. Tabachnikov.
Speaker: Alexander Vainshtein
Institution: U. Haifa
Event Organizer: S. Fomin