- Speaker(s)
- Xiao Zhong
- Affiliation
- School of Mathematics, Sun Yat-sen University
- Language of the talk
- English
- Date
- Nov. 27, 2025, 12:30 p.m.
- Room
-
room 5070
- Seminar
- Seminar of Mathematical Physics Equations Group
We study the variational problem associated with dimer models, a class of models from integrable probability and statistical mechanics in dimension two, which have been the focus of intense research efforts over the last decades. These models give rise to an infinite family of
non-differentiable functionals on Lipschitz functions with gradient constraint, determined by solutions of the Dirichlet problem on compact convex polygons for a class of Monge-Ampère equations. We settle several outstanding open questions for this infinite class of functionals. In articular, we prove a complete classification of the regularity of minimizers, also known as height functions, for all dimer models for a natural class of polygonal (simply or multiply connected) domains, much studied in numerical simulations and elsewhere.
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