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Integrable systems blackboard seminar
Integrable systems blackboard seminar
Orthogonal ring patterns, discrete surfaces and integrable systems
Orthogonal ring patterns, discrete surfaces and integrable systems
Organizers
Speaker
Alexander Bobenko
Time
Monday, April 13, 2026 3:30 PM - 4:30 PM
Venue
A7-201
Abstract
We introduce orthogonal ring patterns consisting of pairs of concentric circles. They generalize orthogonal circle patterns which can be treated as a conformal limit. It is shown that orthogonal ring patterns in Euclidean and hyperbolic planes and in a sphere are governed by discrete integrable equations. We deliver variational principles which are used to prove existence and uniqueness results, and also to compute ring patterns with classical boundary conditions. The later are used to generate discrete constant mean curvature surfaces. The relation to minimal surfaces in S3 and AdS3 is discussed. Numerous models will be presented.
The talk is based on:A.I. Bobenko, Spherical and hyperbolic orthogonal ring patterns: Integrable systems and variational principles, Trans. AMS (2025) A.I. Bobenko, T. Hoffmann, N. Smeenk, Discrete constant mean curvature surfaces and orthogonal ring patterns. Geometry from
combinatorics, arXiv:2410.08915 (2024)
The talk is based on:A.I. Bobenko, Spherical and hyperbolic orthogonal ring patterns: Integrable systems and variational principles, Trans. AMS (2025) A.I. Bobenko, T. Hoffmann, N. Smeenk, Discrete constant mean curvature surfaces and orthogonal ring patterns. Geometry from
combinatorics, arXiv:2410.08915 (2024)
Speaker Intro
Alexander Bobenko is a distinguished Professor of Mathematics at the Technische Universität Berlin, Germany, renowned for his contributions to geometry, mathematical physics, and their applications. His research spans a wide array of topics, including differential geometry, discrete differential geometry, integrable systems, Riemann surfaces, and geometry processing. With an impressive publication record in top-tier journals such as *Annals of Mathematics*, *Duke Mathematical Journal*, *Journal of Differential Geometry*, *Geometry & Topology*, *Advances in Mathematics*, and *Crelle's Journal*, Professor Bobenko has established himself as a leading figure in his field.
From 2012 to 2024, he led the DFG Transregional Collaborative Research Center "Discretization in Geometry and Dynamics". Currently, he is on the Executive Board of the Berlin Mathematical School and a member of the DFG Research Center "Matheon," further solidifying his role in shaping the future of mathematical research and education.