3 citations · 7 across the 9 of their papers we have counts for
11 papers
Möbius Invariant Dimers and Miquel Dynamics
Niklas C. Affolter, Luis Mühlhoff
As is already known, there is a correspondence between circle patterns and the dimer model, which is invariant under Euclidean transformations. We establish a new correspondence th…
Discrete Koenigs nets, inscribed quadrics and autoconjugate curves
Niklas Christoph Affolter, Alexander Yves Fairley
Discrete Koenigs nets are a special class of discrete surfaces that play a fundamental role in discrete differential geometry, in particular in the study of discrete isothermic and…
Discrete Koenigs nets and finite Laplace sequences
Niklas Christoph Affolter, Alexander Yves Fairley
Q-nets are maps from the square grid to projective space that have planar faces. We consider the Laplace sequences of Q-nets, which are determined by iterating a discrete time dyna…
Discrete Lorentz surfaces and s-embeddings II: maximal surfaces
Niklas Christoph Affolter, Felix Dellinger, Christian Müller +2
S-embeddings were introduced by Chelkak as a tool to study the conformal invariance of the thermodynamic limit of the Ising model. Moreover, Chelkak, Laslier and Russkikh introduce…
Discrete Lorentz surfaces and s-embeddings I: isothermic surfaces
Niklas Christoph Affolter, Felix Dellinger, Christian Müller +2
S-embeddings were introduced by Chelkak as a tool to study the conformal invariance of the thermodynamic limit of the Ising model. Moreover, Chelkak, Laslier and Russkikh introduce…
Principal binets
Niklas Christoph Affolter, Jan Techter
Conjugate line parametrizations of surfaces were first discretized almost a century ago as quad meshes with planar faces. With the recent development of discrete differential geome…
Möbius invariant Y-systems (cluster structures) for Miquel dynamics
Niklas Christoph Affolter
Miquel dynamics is a discrete time dynamics for circle patterns, which relies on Miquel's six circle theorem. Previous work shows that the evolution of the circle centers satisfy t…
Discrete Differential Geometry and Cluster Algebras via TCD maps
Niklas Christoph Affolter
In this PhD thesis we develop the frame work of triple crossing diagram maps (TCD maps), which describes constrained configurations of points in projective spaces and discrete dyna…
The Schwarzian octahedron recurrence (dSKP equation) II: geometric systems
Niklas Christoph Affolter, Béatrice de Tilière, Paul Melotti
We consider nine geometric systems: Miquel dynamics, P-nets, integrable cross-ratio maps, discrete holomorphic functions, orthogonal circle patterns, polygon recutting, circle inte…
The Schwarzian octahedron recurrence (dSKP equation) I: explicit solutions
Niklas Christoph Affolter, Béatrice de Tilière, Paul Melotti
We prove an explicit expression for the solutions of the discrete Schwarzian octahedron recurrence, also known as the discrete Schwarzian KP equation (dSKP), as the ratio of two pa…
Miquel Dynamics, Clifford Lattices and the Dimer Model
Niklas C. Affolter
Miquel dynamics were introduced by Ramassamy as a discrete time evolution of square grid circle patterns on the torus. In each time step every second circle in the pattern is repla…