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Quantization of bending deformations of polygons in E3,hypergeometric in tegrals and the Gassner representation
bending deformations of polygons E3 hypergeometric in tegrals the Gassner representation
2015/10/14
Quantization of bending deformations of polygons in E3,hypergeometric in tegrals and the Gassner representation.
THE SYMPLECTIC GEOMETRY OF POLYGONS IN THE 3-SPHERE
SYMPLECTIC GEOMETRY POLYGONS 3-SPHERE
2015/10/14
THE SYMPLECTIC GEOMETRY OF POLYGONS IN THE 3-SPHERE.
THE SYMPLECTIC GEOMETRY OF POLYGONS IN HYPERBOLIC 3-SPACE
SYMPLECTIC GEOMETRY POLYGONS HYPERBOLIC 3-SPACE
2015/10/14
THE SYMPLECTIC GEOMETRY OF POLYGONS IN HYPERBOLIC 3-SPACE.
The Toric Geometry of Triangulated Polygons in Euclidean Space
Toric Geometry Triangulated Polygons Euclidean Space
2015/10/14
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
Symplectic Geometry Polygons Euclidean Space
2015/10/14
The Symplectic Geometry of Polygons in Euclidean Space.
ON THE MODULI SPACE OF POLYGONS IN THE EUCLIDEAN PLANE
MODULI SPACE POLYGONS EUCLIDEAN PLANE
2015/10/14
ON THE MODULI SPACE OF POLYGONS IN THE EUCLIDEAN PLANE.
Polygons in Minkowski three space and parabolic Higgs bundles of rank two on CP^1
Polygons Minkowski space parabolic bundle Higgs field hyperpolygons
2012/6/29
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 ...
Lattice multi-polygons
Lattice polygon twelve-point theorem Pick’s formula Ehrhart polynomial toric topology
2012/4/17
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...
Liouville-Arnold integrability of the pentagram map on closed polygons
Liouville-Arnold integrability closed polygons Dynamical Systems
2011/9/14
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 ...
Integrable Hamiltonian systems with incomplete flows and Newton's polygons
integrable Hamiltonian system incomplete Hamiltonian flows Newton’s polygon
2011/9/1
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...
Unsolved Problems in Visibility Graphs of Points, Segments and Polygons
Unsolved Problems Visibility Graphs of Points Segments Polygons
2011/3/3
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.
Triangulations of nearly convex polygons
triangulation convex set triangulation polynomial
2011/1/20
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...