Instructors/Speakers
Prof. Anton DZHAMAY
Professor
School of Mathematical Sciences
College of Natural and Health Sciences
University of Northern Colorado
U.S.A.
Abstract
Many interesting examples of discrete integrable systems can be studied from the geometric point of view. In this talk we will consider two classes of examples of such system: autonomous (QRT maps) and non-autonomous (discrete Painlevé equations). We introduce some geometric tools to study such systems, such as the blowup procedure to construct algebraic surfaces on which the mappings are regularized, linearization of the mapping on the Picard lattice of the surface and, for discrete Painlevé equations, the decomposition of the Picard lattice into complementary pairs of the surface and symmetry sub-lattices and construction of a binational representation of affine Weyl symmetry groups that gives a complete algebraic description of our non-linear dynamic.
Biography
Prof. Anton Dzhamay got his undergraduate degree from Moscow Institute of Electronics and Mathematics and his PhD degree from Columbia University under the direction of Professor Igor Krichever. After a postdoc position at the University of Michigan in Ann Arbor, where he worked with Professor Igor Dolgachev, Anton moved to the University of Northern Colorado in 2005, where he is currently a Full Professor. Anton is interested in applications of algebro-geometric techniques to the study of various problems related to the theory of integrable systems and soliton equations, such as theory of Frobenius manifolds and WDVV equations, Whitham hierarchies, isospectral and isomonodromic transformations, and so on. Over the last 10 years his research has been on the geometric theory of discrete Painlevé equations (Sakai’s Theory) and its various applications.