Related papers: Moore's Conjecture for Polyhedral Products
A conjecture of Cigler which realizes normalized q-Hermite polynomials as moments is verified.
In this paper we consider the linear second order partial differential equation with non-constant coefficients; then by using the double convolution product we produce new equations with polynomials coefficients and we classify the new…
In this note, we show that the strong Viterbo conjecture holds true on any convex toric domain, and that the Viterbo's volume-capacity conjecture holds for the product of a $1$-unconditional convex body $A\subset\mathbb{R}^{n}$ and its…
The Volume conjecture claims that the hyperbolic Volume of a knot is determined by the colored Jones polynomial. The purpose of this article is to show a Volume-ish theorem for alternating knots in terms of the Jones polynomial, rather than…
This paper investigates the rigidity of bordered polyhedral surfaces. Using the variational principle, we show that bordered polyhedral surfaces are determined by boundary value and discrete curvatures on the interior edges. As a corollary,…
We give a geometric method for determining the cohomology groups of a polyhedral product under suitable freeness conditions or with coefficients taken in a field. This is done by considering first the special case for which the pairs of…
Eberhard-type theorems are statements about the realizability of a polytope (or more general polyhedral maps) given the valency of its vertices and sizes of its polygonal faces up to a linear linear degree of freedom. We present new…
The Gauss-Bonnet theorem for a polyhedron (a union of finitely many compact convex polytopes) in $n$-dimensional Euclidean space expresses the Euler characteristic of the polyhedron as a sum of certain curvatures, which are different from…
A combinatorial construction is used to analyze the properties of polyhedral products and generalized moment-angle complexes with respect to certain operations on CW pairs including exponentiation. This allows for the construction of…
In this paper for a class of symmetric multiparty pure states we consider a conjecture related to the geometric measure of entanglement: 'for a symmetric pure state, the closest product state in terms of the fidelity can be chosen as a…
We investigate the rigidity of hyperbolic cone metrics on $3$-manifolds which are isometric gluing of ideal and hyper-ideal tetrahedra in hyperbolic spaces. These metrics will be called ideal and hyper-ideal hyperbolic polyhedral metrics.…
A polytrope is a tropical polytope which at the same time is convex in the ordinary sense. A $d$-dimensional polytrope turns out to be a tropical simplex, that is, it is the tropical convex hull of $d+1$ points. This statement is equivalent…
The Gaussian Correlation Conjecture states that for any two symmetric, convex sets in n-dimensional space and for any centered, Gaussian measure on that space, the measure of the intersection is greater than or equal to the product of the…
The main result of this paper states that a symplectic s-cobordism of elliptic 3-manifolds is diffeomorphic to a product (assuming a canonical contact structure on the boundary). Based on this theorem, we conjecture that a smooth…
Watkins' conjecture asserts that the rank of an elliptic curve is upper bounded by the $2$-adic valuation of its modular degree. We show that this conjecture is satisfied when $E$ is any quadratic twist of an elliptic curve with rational…
In this survey article, we summarise the known results towards the conjecture: elliptic curves over totally real number fields are modular. For understanding these recent results in the literature, we present some necessary background along…
We prove that a 3-dimensional hyperbolic cusp with convex polyhedral boundary is uniquely determined by the metric induced on its boundary. Furthemore, any hyperbolic metric on the torus with cone singularities of positive curvature can be…
This is an introduction to the Volume Conjecture and its generalizations for nonexperts. The Volume Conjecture states that a certain limit of the colored Jones polynomial of a knot would give the volume of its complement. If we deform the…
We prove that if the Morrison cone conjecture holds for a smooth Calabi-Yau threefold $Y$, it holds for any smooth Calabi-Yau threefold deformation-equivalent to $Y$. We use this result to prove a new case of the Morrison cone conjecture.
We obtain a classification of metaplectic modular categories: every metaplectic modular category is a gauging of the particle-hole symmetry of a cyclic modular category. Our classification suggests a conjecture that every weakly-integral…