Related papers: Three-dimensional terminal toric flips
We construct a positive-dimensional, reducible Severi variety on a toric surface.
In this paper we study the structure of $k$-transitive closures of directed paths and formulate several properties. Concept of $k$-transitive orientation generalize the traditional concept of transitive orientation of a graph.
We study with first-principles methods the interplay between bulk and surface Dirac fermions in three dimensional Dirac semimetals. By combining density functional theory with the coherent potential approximation, we reveal a topological…
Scroll waves exist ubiquitously in three-dimensional excitable media. It's rotation center can be regarded as a topological object called vortex filament. In three-dimensional space, the vortex filaments usually form closed loops, and even…
Tight triangulated manifolds are generalisations of neighborly triangulations of closed surfaces and are interesting objects in Combinatorial Topology. Tight triangulated manifolds are conjectured to be minimal. Except few, all the known…
We describe the structure of the algebraic group of automorphisms of all simple finite dimensional Lie superalgebras. Using this and \'etale cohomology considerations, we list all different isomorphism classes of the corresponding twisted…
We introduce a theoretical framework for the new concept of three-dimensional (3D) twistronics by developing a generalized Bloch band theory for 3D layered systems with a constant twist angle $\theta$ between successive layers. Our theory…
For each closed oriented 3-manifold $M$ in Thurston's picture, the set of degrees of self-maps on $M$ is given.
In this note we collect some results on the deformation theory of toric Fano varieties.
The recent discovery of higher-order topology has largely enriched the classification of topological materials. Theoretical and experimental studies have unveiled various higher-order topological insulators that exhibit topologically…
Conformal mapping is an important mathematical tool in many physical and engineering fields, especially in electrostatics, fluid mechanics, classical mechanics, and transformation optics. However in the existing textbooks and literatures,…
The relevance of two-dimensional three-components (2D3C) flows goes well beyond their occurrence in nature, and a deeper understanding of their dynamics might be also helpful in order to shed further light on the dynamics of pure…
Finite real spectral triples are defined to characterise the non-commutative geometry of a fuzzy torus. The geometries are the non-commutative analogues of flat tori with moduli determined by integer parameters. Each of these geometries has…
We study the geometry of spaces of planes on smooth complete intersections of three quadrics, with a view toward rationality questions.
We classify the terminal Fano threefolds of Picard number one that come with an effective action of a two-torus. Our approach applies also to higher dimensions and generalizes the correspondence between toric Fano varieties and lattice…
We present a simple visual description of the topology of the space of three-dimensional rotations, requiring just intuition, imagination and no advanced math.
We study the pattern of three state topological phases that appear in systems with real Hamiltonians and wave functions. We give a simple geometric construction for representing these phases. We then apply our results to understand previous…
The transition from two-dimensional to three-dimensional flows in a finite circular cylinder driven by an axially oscillating sidewall is explored in detail. The complete symmetry group of this flow, including a spatio-temporal symmetry…
Applications of the three-dimensional transformation for rotating coordinate systems to quantum mechanics, general theory relativity and optics are considered.
We study finite dimensional representations of the projective modular group. Various explicit dimension formulas are given.