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Quantization of bending deformations of polygons in E3,hypergeometric in tegrals and the Gassner representation.
THE SYMPLECTIC GEOMETRY OF POLYGONS IN THE 3-SPHERE.
THE SYMPLECTIC GEOMETRY OF POLYGONS IN HYPERBOLIC 3-SPACE.
Speyer and Sturmfels associated Grobner toric degenerations Gr¨2(Cn)T of Gr2(Cn) witheach trivalent tree T having n leaves. These degenerations induce toric degenerations Mr T of Mr, the space of n or...
The Symplectic Geometry of Polygons in Euclidean Space.
ON THE MODULI SPACE OF POLYGONS IN THE EUCLIDEAN PLANE.
Consider the moduli space of parabolic Higgs bundles (E,\Phi) of rank two on CP^1 such that the underlying holomorphic vector bundle for the parabolic vector bundle E is trivial. It is equipped with t...
The early Renaissance artist Albrecht Durer published a book on geometry a few years before he died. This was intended to be a guide for young craftsmen and artists giving them both practical and math...
We describe two different approaches to making systematic classifications of plane lattice polygons, and recover the toric codes they generate, over small fields, where these match or exceed the best ...
We discuss generalizations of some results on lattice polygons to certain piecewise linear loops which may have a self-intersection but have vertices in the lattice $\Z^2$. We first prove a formula on...
Abstract: The pentagram map is a discrete dynamical system defined on the moduli space of polygons in the projective plane. This map has recently attracted a considerable interest, mostly because its ...
Abstract: We study the Hamiltonian vector field $v=(-\partial f/\partial w,\partial f/\partial z)$ on $\mathbb C^2$, where $f=f(z,w)$ is a polynomial in two complex variables, which is non-degenerate ...
Abstract: The extension complexity of a polytope $P$ is the smallest integer $k$ such that $P$ is the projection of a polytope $Q$ with $k$ facets. We study the extension complexity of $n$-gons in the...
In this survey paper, we present open problems and conjectures on visibility graphs of points, segments and polygons along with necessary backgrounds for understanding them.
Counting Euclidean triangulations with vertices in a finite set C of the convex hull Conv(C ) of C is difficult in general, both algorithmically and theoretically. The aim of this paper is to describ...

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