To each once-punctured-torus bundle, $T_φ$, over the circle with pseudo-Anosov monodromy $φ$, there are associated two tessellations of the complex plane: one, $Δ(φ)$, is (the projection from $\infty$ of) the triangulation of a horosphere at $\...
We study the modular invariance in magnetized torus models. Modular invariant flavor model is a recently proposed hypothesis for solving the flavor puzzle, where the flavor symmetry originates from modular invariance. In this framework coupling const...
Starting 02/09/2026, you will no longer get an option to select between JIT or debug account on Torus STS as your JIT account will not be elevated. Once authenticated, you will directly be logged into …
The mapping torus induced by an automorphism $φ$ of the free abelian group $\mathbb{Z}^n$ is a semi-direct product $G=\mathbb{Z}^n\rtimes_φ\mathbb{Z}$. We show that whether the rank of $G$ is equal to $n+1$ is decidable. As a corollary, the rank of...
We compute the number of systoles, the shortest simple closed geodesics and 2-systoles, the second shortest simple closed geodesics on hyperbolic surfaces homeomorphic to once-punctured torus and four-punctured sphere....
If M is a hyperbolic once-punctured torus bundle over the circle, then the trace field of M has no real places....
We prove that if $G_φ=\langle F, t| t x t^{-1} =φ(x), x\in F\rangle$ is the mapping torus group of an injective endomorphism $φ: F\to F$ of a free group $F$ (of possibly infinite rank), then every two-generator subgroup $H$ of $G_φ$ is either fre...
The flow of material from Io's volcanoes into the Io plasma torus, out into the magnetosphere, and along field lines into Jupiter's upper atmosphere is not adequately understood. The lack of observations of spatial and temporal variations in the Io p...
Standard models of force balance along Jovian field lines predict the location of the Io plasma torus to be the centrifugal equator of Jupiter's magnetosphere, i.e. the position along the magnetic field lines farthest away from Jupiter's rotational a...
An explicit expression is obtained for the generating series for the number of ramified coverings of the sphere by the torus, with elementary branch points and prescribed ramification type over infinity. This proves a conjecture of Goulden, Jackson...
The width of a convex curve in the plane is the minimal distance between a pair of parallel supporting lines of the curve. In this paper we study the width of nodal lines of eigenfunctions of the Laplacian on the standard flat torus. We prove a varie...
The Peterson variety is a subvariety of the flag manifold $G/B$ equipped with an action of a one-dimensional torus, and a torus invariant paving by affine cells, called Peterson cells. We prove that the equivariant pull-backs of Schubert classes inde...
Let T_n be the Teichmueller space of flat metrics on the n-dimensional torus and identify SL(n,Z) with the corresponding mapping class group. We prove that the subset Y consisting of those points at which the systoles generate the fundamental group...
Models of active galactic nuclei (AGN) suggest that their circumnuclear media are complex with clumps and filaments, while recent observations hint towards polar extended structures of gas and dust, as opposed to the classical torus paradigm. The X-r...
An irreducible 3--manifold with torus boundary either is a Seifert fibered space or admits at most three lens space fillings according to the Cyclic Surgery Theorem. We examine the sharpness of this theorem by classifying the non-hyperbolic manifolds...
Fang and Fourier defined the symplectic Dellac configurations in order to parametrize the torus fixed points of the symplectic degenerated flag varieties, and conjectured that their numbers are the elements of a sequence of integers (1, 2, 10, 98, 15...
For certain bordered submanifolds $M\subset\CC^2$ we show that $M$ can be embedded properly and holomorphically into $\CC^2$. An application is that any subset of a torus with two boundary components can be embedded properly into $\CC^2$....
We consider an irreducible Anosov automorphism L of a torus T^d such that no three eigenvalues have the same modulus. We show that L is locally rigid, that is, L is C^1 conjugate to any C^1-small perturbation f with the same periodic data. We also pr...
Gelfond and Khovanskii found a formula for the sum of the values of a Laurent polynomial over the zeros of a system of n Laurent polynomials in the algebraic n-torus. We expect that a similar formula holds in the case of exponential sums with real...
Using the notion of equivariant Kirwan map, as defined by Goldin, we prove that -- in the case of Hamiltonian torus actions with isolated fixed points -- Tolman and Weitsman's description of the kernel of the Kirwan map can be deduced directly from...