Alfredo Hubard

activity

20102026

most citedConvex Equipartitions: The Spicy Chicken Theorem

48 citations · 91 across the 23 of their papers we have counts for

collaborators

30 papers

math.CO2026

Crossing numbers of simplicial complexes

Alfredo Hubard, Cheikh Saliou Ndiaye, Oriol Solé-Pi

This paper studies crossing numbers of $d$ -dimensional simplicial complexes drawn in $R^{2 d}$ or $S^{2 d}$ . We clarify and generalize a number of known results and c…

math.CO2026

Overlap-Helly theorems

Andreas F. Holmsen, Alfredo Hubard

In this paper we introduce a generalization of Helly's theorem closely connected to Bárány-Gromov overlap theorems (also called selection lemmas). Our main result implies both the…

math.MG2026

Volume and Projection Inequalities I: Zonoids and Courtade's Conjecture

Matthieu Fradelizi, Alfredo Hubard, Auttawich Manui +3

We study volume and projection inequalities for zonoids through the multiaffine determinant polynomials that encode their volumes. We show that a log-submodularity conjecture for t…

math.CO2025

Crossing numbers of dense graphs on surfaces

Alfredo Hubard, Arnaud de Mesmay, Hugo Parlier

In this paper, we provide upper and lower bounds on the crossing numbers of dense graphs on surfaces, which match up to constant factors. First, we prove that if $G$ is a dense eno…

math.GT2025

Crossing number inequalities for curves on surfaces

Alfredo Hubard, Hugo Parlier

We prove that, as $m$ grows, any family of $m$ homotopically distinct closed curves on a surface induces a number of crossings that grows at least like $(m lo g m)^{2}$ . We use this…

math.CO2025

Cubulating the sphere with many facets

Sergey Avvakumov, Alfredo Hubard

For each $d \geq 3$ we construct cube complexes homeomorphic to the $d$ -sphere with $n$ vertices in which the number of facets (assuming $d$ constant) is $Ω (n^{5/4})$ . This disprove…

math.CO2024

Bisecting masses with families of parallel hyperplanes

Alfredo Hubard, Pablo Soberón

We prove a common generalization of several mass partition results using hyperplane arrangements to split $R^{d}$ into two sets. Our main result implies the ham sandwich the…

math.CO2024

Crossing lemmas for $k$ -systems of arcs

Alfredo Hubard, Hugo Parlier

We show a generalization of the crossing lemma for multi-graphs drawn on orientable surfaces in which pairs of edges are assumed to be drawn by non-homotopic simple arcs which pair…

math.MG2023

Weak $(1 - ε)$ -nets for polynomial superlevel sets

Pablo González-Mazón, Alfredo Hubard, Roman Karasev

We prove that for any Borel probability measure $μ$ on $R^{n}$ there exists a set $X \subset R^{n}$ of $n + 1$ points such that any $n$ -variate quadratic polynomial $P$ th…

cs.CG2023

Degenerate crossing number and signed reversal distance

Niloufar Fuladi, Alfredo Hubard, Arnaud de Mesmay

Given a graph drawn in the plane, the degenerate crossing number of the drawing is the number of points in the plane which are contained in the relative interior of at least two ed…

math.CO2022

Disjoint faces in simple drawings of the complete graph and topological Heilbronn problems

Alfredo Hubard, Andrew Suk

Given a complete simple topological graph $G$ , a $k$ -face generated by $G$ is the open bounded region enclosed by the edges of a non-self-intersecting $k$ -cycle in $G$ . Interesting…

cs.CG2022

Short Topological Decompositions of Non-Orientable Surfaces

Niloufar Fuladi, Alfredo Hubard, Arnaud de Mesmay

In this article, we investigate short topological decompositions of non-orientable surfaces and provide algorithms to compute them. Our main result is a polynomial-time algorithm t…

math.MG2021

Systolic inequalities for the number of vertices

Sergey Avvakumov, Alexey Balitskiy, Alfredo Hubard +1

Inspired by the classical Riemannian systolic inequality of Gromov we present a combinatorial analogue providing a lower bound on the number of vertices of a simplicial complex in…

math.MG2019★ 1 cited

Equipartitions and Mahler volumes of symmetric convex bodies

Matthieu Fradelizi, Alfredo Hubard, Mathieu Meyer +2

Following ideas of Iriyeh and Shibata we give a short proof of the three-dimensional Mahler conjecture {\mf for symmetric convex bodies}. Our contributions include, in particular,…

math.PR2019★ 3 cited

Random polytopes and the wet part for arbitrary probability distributions

Imre Bárány, Matthieu Fradelizi, Xavier Goaoc +2

We examine how the measure and the number of vertices of the convex hull of a random sample of $n$ points from an arbitrary probability measure in $R^{d}$ relates to the wet…

math.CO2018

Limits of Order Types

Xavier Goaoc, Alfredo Hubard, Rémi de Joannis de Verclos +2

We apply ideas from the theory of limits of dense combinatorial structures to study order types, which are combinatorial encodings of finite point sets. Using flag algebras we obta…

math.AT2018★ 11 cited

Bisecting measures with hyperplane arrangements

Alfredo Hubard, Roman Karasev

We show that when $n$ is a power of two, any $n D$ measures in $R^{n}$ can be bisected by an arrangement of $D$ hyperplanes.

cs.CG2018

Consistent sets of lines with no colorful incidence

Boris Bukh, Xavier Goaoc, Alfredo Hubard +1

We consider incidences among colored sets of lines in $R^{d}$ and examine whether the existence of certain concurrences between lines of $k$ colors force the existence of at…

math.CO2017★ 1 cited

On a topological version of Pach's overlap theorem

Boris Bukh, Alfredo Hubard

Pach showed that every $d + 1$ sets of points $Q_{1}, \dots, Q_{d + 1} \subset R^{d}$ contain linearly-sized subsets $P_{i} \subset Q_{i}$ such that all the transversal simplices that t…

math.DG2016★ 11 cited

Lower and upper bounds for the waists of different spaces

Arseniy Akopyan, Alfredo Hubard, Roman Karasev

We prove several new results around Gromov's waist theorem. We give a simple proof of Vaaler's theorem on sections of the unit cube using the Borsuk--Ulam--Crofton technique. We co…

cs.CG2016

Shortest path embeddings of graphs on surfaces

Alfredo Hubard, Vojtěch Kaluža, Arnaud de Mesmay +1

The classical theorem of Fáry states that every planar graph can be represented by an embedding in which every edge is represented by a straight line segment. We consider generaliz…

math.MG2014

Realization spaces of arrangements of convex bodies

Michael Gene Dobbins, Andreas Holmsen, Alfredo Hubard

We introduce combinatorial types of arrangements of convex bodies, extending order types of point sets to arrangements of convex bodies, and study their realization spaces. Our mai…

math.CO2014

Discrete Systolic Inequalities and Decompositions of Triangulated Surfaces

Éric Colin de Verdière, Alfredo Hubard, Arnaud de Mesmay

How much cutting is needed to simplify the topology of a surface? We provide bounds for several instances of this question, for the minimum length of topologically non-trivial clos…

math.MG2013

Regular systems of paths and families of convex sets in convex position

Michael G. Dobbins, Andreas F. Holmsen, Alfredo Hubard

In this paper we show that every sufficiently large family of convex bodies in the plane has a large subfamily in convex position provided that the number of common tangents of eac…