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Integrable systems blackboard seminar
Integrable systems blackboard seminar
Dimers and M-curves: Limit shapes from Riemann surfaces.
Dimers and M-curves: Limit shapes from Riemann surfaces.
Organizers
Speaker
Alexander Bobenko
Time
Monday, May 18, 2026 3:30 PM - 4:30 PM
Venue
A7-201
Abstract
We develop a general approach to solution of the inverse problem for dimer models, in particular explicit description of limit shapes for the Aztec diamond. This leads to dimer models on doubly periodic bipartite graphs with quasiperiodic positive weights. Dimer models with periodic weights and their algebro-geometric description by Kenyon and Okounkov via Harnack curves are recovered as a special case. This generalization from Harnack curves to general M-curves, which are in the focus of our approach, leads to transparent algebro-geometric structures. In particular, using variational descriptions, explicit representations for limit shapes are obtained in terms of Abelian integrals. Based on Schottky uniformization of Riemann surfaces, we compute the weights and dimer configurations. The computational results are in complete agreement with the theoretical predictions. The talk is based on joint works with N. Bobenko and Yu. Suris.
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.