33 citations · 49 across the 8 of their papers we have counts for
9 papers
Intersection Bodies of Polytopes: Translations and Convexity
Marie-Charlotte Brandenburg, Chiara Meroni
We continue the study of intersection bodies of polytopes, focusing on the behavior of under translations of . We introduce an affine hyperplane arrangement and show that t…
Convex Hulls of Curves: Volumes and Signatures
Carlos Améndola, Darrick Lee, Chiara Meroni
Taking the convex hull of a curve is a natural construction in computational geometry. On the other hand, path signatures, central in stochastic analysis, capture geometric propert…
Convex hulls of surfaces in fourspace
Chiara Meroni, Kristian Ranestad, Rainer Sinn
This is a case study of the algebraic boundary of convex hulls of varieties. We focus on surfaces in fourspace to showcase new geometric phenomena that neither curves nor hypersurf…
On smooth functions with two critical values
Antonio Lerario, Chiara Meroni, Daniele Zuddas
We prove that every smooth closed manifold admits a smooth real-valued function with only two critical values. We call a function of this type a \emph{Reeb function}. We prove that…
Quantum Correlations in the Minimal Scenario
Thinh P. Le, Chiara Meroni, Bernd Sturmfels +2
In the minimal scenario of quantum correlations, two parties can choose from two observables with two possible outcomes each. Probabilities are specified by four marginals and four…
The Geometry of Discotopes
Fulvio Gesmundo, Chiara Meroni
We study a class of semialgebraic convex bodies called discotopes. These are instances of zonoids, objects of interest in real algebraic geometry and random geometry. We focus on t…
Intersection Bodies of Polytopes
Katalin Berlow, Marie-Charlotte Brandenburg, Chiara Meroni +1
We investigate the intersection body of a convex polytope using tools from combinatorics and real algebraic geometry. In particular, we show that the intersection body of a polytop…
Fiber Convex Bodies
Léo Mathis, Chiara Meroni
In this paper we study the fiber body, that is the extension of the notion of fiber polytopes for more general convex bodies. After giving an overview of the properties of the fibe…
Real Lines on Random Cubic Surfaces
Rida Ait El Manssour, Mara Belotti, Chiara Meroni
We give an explicit formula for the expectation of the number of real lines on a random invariant cubic surface, i.e. a surface defined by a random gaussia…