7 papers
Integrability of Cauchy problems for discrete conformal maps and circle patterns
Maxim Arnold, Anton Izosimov
A map from a square lattice to the Riemann sphere is called discrete conformal if the image of every elementary square is a harmonic quadrilateral. We prove that the initial value…
Virasoro extensions for diffeomorphisms with breaks
Anton Izosimov, Boris Khesin, Howard Xiao
We study homeomorphisms of the circle that are smooth diffeomorphisms away from a finite set of points. These "broken diffeomorphisms" do not form a Lie group, but instead natu…
Surface topology and incidence theorems over division rings
Anton Izosimov
Incidence theorems concern configurations of points, lines, and, more generally, higher-dimensional subspaces in projective space. Broadly speaking, such theorems fall into two cla…
The dimer model and dynamical incidence geometry
Anton Izosimov, Pavlo Pylyavskyy
We propose a geometric counterpart of the dimer model on bipartite graphs. A state of our model consists of a choice of a point for each white vertex and hyperplane for each black…
Pentagram maps over rings, Grassmannians, and skewers
Leaha Hand, Anton Izosimov
The pentagram map is a discrete dynamical system on planar polygons. By definition, the image of a polygon under the pentagram map is the polygon whose vertices are the in…
Planar networks and simple Lie groups beyond type A
Anton Izosimov
The general linear group , along with its adjoint simple group , can be described by means of weighted planar networks. In this paper we give a network description f…