Related papers: Taxicab Butterflies
Geometric structures on manifolds became popular when Thurston used them in his work on the geometrization conjecture. They were studied by many people and they play an important role in higher Teichm\"uller theory. Geometric structures on…
We extend the formality theorem of Maxim Kontsevich from deformations of the structure sheaf on a manifold to deformations of gerbes on smooth and complex manifolds.
A foundation is laid for a theory of combinatorial groupoids, allowing us to use concepts like ``holonomy'', ``parallel transport'', ``bundles'', ``combinatorial curvature'' etc. in the context of simplicial (polyhedral) complexes, posets,…
We experimentally realize higher-order catastrophic structures in light fields to access the rich class of caustic swallowtail and butterfly beams. These beams present solutions of paraxial diffraction catastrophe integrals that are…
In this study, after introducing algebraic properties of real quaternions some characterizations of quaternionic involute-evolute curves in Q are obtained. And some results and theorems for quaternionic w-curves are given. Lastly, we…
We study the lattices of algebraic and transcendental cycles of cubic fourfolds.
A short proof of the Mazur-Ulam theorem concerning isometries of real normed spaces.
A family of polynomials linked to the set of the deltoid tangents and its associated algebraic hypersurfaces has been presented in recent years. In this paper we study some related maximising and free plane curves. We also analyse the…
We discuss the notion of the orbifold transform, and illustrate it on simple examples. The basic properties of the transform are presented, including transitivity and the exponential formula for symmetric products. The connection with the…
The Helfrich's shape equation of axisymmetric vesicles is studied. A sufficient condition on the physical parameters and some geometric properties are discovered for the biconcave shape.
We give an account, in terms of fibered categories and their fibrewise duals, of aspects of the theory of bundle functors and star-bundle functors in differential geometry.
An algebraic deformation theory of dialgebra morphisms is obtained.
Honeycomb toroidal graphs are trivalent Cayley graphs on generalized dihedral groups. We examine the two historical threads leading to these graphs, some of the properties that have been established, and some open problems.
Various aspects of Supersymmetry in 1-dimensional systems are analyzed.
The link between Tauberian theorems and large deviations is surveyed, with particular reference to regular variation.
We give a stochastic generalization of transport theorem on smooth manifold. Furthermore, we deduce a system of continuity equation and present some application on torus.
An introduction to moduli spaces of representations of quivers is given, and results on their global geometric properties are surveyed. In particular, the geometric approach to the problem of classification of quiver representations is…
This is a survey of the theory of real trees and their applications.
This paper is a sequel to [3]. We formulate a natural algebraic geometry conjecture, give some of its number theoretic and analytical consequences, and show that those can be used to get further advances in wave turbulence theory.
This paper is a gentle introduction to some recent results involving the theory of gerbes over orbifolds for topologists, geometers and physicists. We introduce gerbes on manifolds, orbifolds, the Dixmier-Douady class, Beilinson-Deligne…