Geometry of the Doubly Periodic Aztec Dimer Model
Explore the geometry of the doubly periodic Aztec diamond dimer model, including arctic curves, amoeba, and local fluctuations in statistical mechanics and discrete geometry.
The Multinomial Dimer Model - Statistical Mechanics and Discrete Geometry
Explore the multinomial dimer model's limit shape theory, bistochastic gauge, and 3D Aztec diamond applications in statistical mechanics and discrete geometry.
Spectrum of the Ising Model
Explore the correspondence between Ising models and algebro-geometric data, extending Kenyon and Okounkov's work on dimer models and Harnack curves in this advanced mathematical presentation.
Minimal Bipartite Dimers and Maximal Riemann Surfaces
Exploration of critical weights for dimer models on isoradial graphs, extending Kenyon's results using theta functions on maximal Riemann surfaces, with applications to spectral theorems and Laplacians.
Causal Set Kinematics: Reconstructing Spacetime Geometry from Random Posets
Explore causal set quantum gravity, reconstructing spacetime geometry from random posets. Learn dimension estimation, topology, and geometric invariants in discrete orders.