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Integrable systems blackboard seminar
Quantum Minimal Surfaces and Discrete Painlevé equations
Quantum Minimal Surfaces and Discrete Painlevé equations
演讲者
时间
2025年12月15日 15:20 至 16:30
地点
A7-201
摘要
In a preprint arXiv:1903.10792 J.Arnlind, J.Hoppe and M.Kontsevich discussed analogues of quantum minimal surfaces. In some examples, characterizing such objects reduces to describing solutions of certain recurrence relations satisfying the positivity requirement. When these recurrences are non-linear, this is a very difficult question. In a special case where classical minimal surface corresponds to the complex parabola, this recurrence turns out to be a particular example of a discrete Painlevé equation. In this talk I will explain how the geometric approach to Painlevé equations allows us to show the existence of a unique positive solution of this equation and, moreover, explicitly characterize it. This is a joint work with Andy Hone, Peter Clarkson, and Ben Mitchell (arXiv:2503.14436, TMPh 244 (2025)).
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.