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BIMSA Integrable Systems Seminar
Geometry of Discrete Integrable Systems: QRT Maps and Discrete Painlevé Equations
Geometry of Discrete Integrable Systems: QRT Maps and Discrete Painlevé Equations
演讲者
时间
2023年03月03日 17:00 至 18:30
地点
A6-101
摘要
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 these 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 birational representation of affine Weyl symmetry groups that gives a complete algebraic description of our non-linear dynamic.
This talk is based on joint work with Stefan Carstea (Bucharest) and Tomoyuki Takenawa (Tokyo).
演讲者介绍
Anton Dzhamay received his undergraduate education in Moscow where he graduated from the Moscow Institute of Electronics and Mathematics (MIEM) in 1993. He got his PhD from Columbia University under the direction of Professor Igor Krichever in 2000. After having postdoc and visiting positions at the University of Michigan and Columbia University, Anton moved to the University of Northern Colorado, getting tenure in 2011, becoming a Full Professor in 2016, and now transitioning to the Emeritus status in 2025. In 2023–2024 Anton was also a Visiting Professor at BIMSA, he became a permanent BIMSA faculty in Summer 2024 . His research interests are focused on the application of algebro-geometric techniques to integrable systems. Most recently he has been working on discrete integrable systems, Painlevé equations, and applications.