Geometry of Discrete Integrable Systems
This course is an introduction to some modern ideas of the geometric approach to two-dimensional discrete integral systems. We primarily focus on two main classes of such systems — the QRT maps that are autonomous discrete systems, and discrete Painlevé equations, that are non-autonomous. Studying these systems nicely ties together tools and techniques from complex algebraic and differential geometry, and the theory of root systems, affine Weyl groups, and their birational representations. These equations have a wide range of modern applications, in particular in integrable systems, theory of orthogonal polynomials, and in integrable probability, as well as more exotic applications, e.g., characterization of some quantum minimal surfaces.
Lecturer
Date
15th September, 2026 ~ 5th January, 2027
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Tuesday,Thursday | 11:00 - 12:30 | Shuangqing | - | - | - |
Audience
Advanced Undergraduate
, Graduate
, Postdoc
, Researcher
Video Public
Yes
Notes Public
Yes
Language
English
Lecturer Intro
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.