About me

I am Professor Titular (associate professor) at the Combinatorics Research Group of the Departament de Matemàtiques i Informàtica at Universitat de Barcelona. I am a member of the IMUB and of the CRM.

I am on leave from my position of Maitre de conférences HDR (associate professor) at Institut de Mathématiques de Jussieu - Paris Rive Gauche at Sorbonne Université, member of the team Combinatoire et Optimisation.

Contact

Arnau Padrol picture by Moritz Firsching at GMZ60

Postal address:

Departament de Matemàtiques i Informàtica
Universitat de Barcelona
Gran via de les Corts Catalanes 585
08007 Barcelona

Office:

P2 39 Edifici històric

Phone:

(+34) 93 402 16 54

E-mail:

arnau dot padrol at ub dot edu.

Research Interests

Discrete and combinatorial geometry. In particular: oriented matroids, convex polytopes and their triangulations, and their applications.

Research

Recent Projects

Publications

Arnau Padrol and Eva Philippe
Sweeps, polytopes, oriented matroids, and allowable graphs of permutations
Appeared in Combinatorica (2023) (online first).
A preprint is available at the arXiv.
Arnau Padrol, Vincent Pilaud, and Germain Poullot
Deformed graphical zonotopes
Appeared in Discrete and Computational Geometry (2023) (online first).
A preprint is available at the arXiv.
An extended abstract appeared in Deformation cones of hypergraphic polytopes in Séminaire Lotharingien de Combinatoire 86B (2022), Art. #72, 12pp. Proc. of 34th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2022) .
Another extended abstract appeared in Proceedings of the Discrete Mathematics Days (DMD 22), 2022, pp. 217–223.
Arnau Padrol, Eva Philippe and Franisco Santos
Many regular triangulations and many polytopes
Appeared in the Mathematische Annalen (2023) (online first).
A preprint is available at the arXiv.
An extended abstract appeared in in Proceedings of the Discrete Mathematics Days (DMD 22), 2022, pp. 211–216.
Arnau Padrol, Yann Palu, Vincent Pilaud and Pierre-Guy Plamondon
Associahedra for finite type cluster algebras and minimal relations between g-vectors
Appeared in the Proceedings of the London Mathematical Society 127 (2023), no. 3, 513–588.
A preprint is available at the arXiv.
An extended abstract appeared as On type cones of g-vector fans in Séminaire Lotharingien de Combinatoire 84B (2020), Art. #13, 12pp. Proc. of 32nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2020) .
Federico Castillo, Jean-Philippe Labbé, Julia Liebert, Arnau Padrol, Eva Philippe, and Christian Schilling
An effective solution to convex 1-body N-representability
Appeared in the Annales Henri Poincaré 24 (2023), no. 7, 2241–2321.
A preprint is available at the arXiv.
Arnau Padrol, Vincent Pilaud, and Germain Poullot
Deformation cones of graph associahedra and nestohedra
Appeared in the European Journal of Combinatorics 107 (2023), Paper No. 103594.
A preprint is available at the arXiv.
An extended abstract appeared in Deformation cones of hypergraphic polytopes in Séminaire Lotharingien de Combinatoire 86B (2022), Art. #72, 12pp. Proc. of 34th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2022) .
Another extended abstract appeared as Computing the type cone of nestohedra in Proc. XIX Spanish Meeting on Computational Geometry, 2021, p. 21.
Arnau Padrol, Vincent Pilaud, and Julian Ritter
Shard Polytopes
Appeared in International Mathematics Research Notices (2022), no. 9, 7686–7796, rnac042.
A preprint is available at the arXiv.
An extended abstract appeared in Séminaire Lotharingien de Combinatoire 85B (2021), Art. #11, 12pp. Proc. of 33rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2021) .
Leonardo Martínez-Sandoval and Arnau Padrol
The convex dimension of hypergraphs and the hypersimplicial Van Kampen-Flores Theorem
Appeared in the Journal of Combinatorial Theory, Series B 149 (2021), pp. 23–51.
A preprint is available at the arXiv.
Erratum: The proof of Theorem 6.5 is wrong. Currently, we do not have any non-trivial upper bound for the d ≤ k regime for non-complete graphs. This does not affect the main results of the paper. We are very grateful to Brett Leroux for pointing out this mistake.
An extended abstract appeared as The convex dimension of k-uniform hypergraphsProc. XVIII Spanish Meeting on Computational Geometry, 2019, pp. 21–24.
Cesar Ceballos, Arnau Padrol and Camilo Sarmiento
The ν-Tamari lattice via ν-trees, ν-bracket vectors, and subword complexes
Appeared in the Electronic Journal of Combinatorics 27 (2020), no. 1, #P1.14, 31.
A preprint is available at the arXiv.
An extended abstract appeared as ν-Tamari lattices via subword complexes in Electronic Notes in Discrete Mathematics 61 (2017), no. Supplement C, 215–221 Proc. of the European Conference on Combinatorics, Graph Theory and Applications (EUROCOMB’17) , Vienna, August 28 - September 1, 2017.
Jeffrey C. Lagarias, Yusheng Luo, and Arnau Padrol
Moser’s Shadow Problem
Appeared in L’Enseignement Mathématique 64 (2018), no. 3-4, 477–496.
A preprint is available at the arXiv.
Cesar Ceballos, Arnau Padrol and Camilo Sarmiento
Geometry of ν-Tamari lattices in types A and B
Appeared in Transactions of the American Mathematical Society 371 (2019), 2575 – 2622.
A preprint is available at the arXiv.
An extended abstract appeared in Séminaire Lotharingien de Combinatoire 78B (2017), Art. 68, 12. Proc. of 29th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2017) .
Another extended abstract appeared as Tropical Catalan subdivisions in Proc. Discrete Mathematics Days - JMDA16 , Barcelona, 2016, pp. 187-192.
Karim A. Adiprasito, Philip Brinkmann, Arnau Padrol, Pavel Paták, Zuzana Patáková, Raman Sanyal
Colorful simplicial depth, Minkowski sums, and generalized Gale transforms
Appeared in International Mathematics Research Notices (2017), rnx184.
A preprint is available at the arXiv.
Francesco Grande, Arnau Padrol and Raman Sanyal
Extension complexity and realization spaces of hypersimplices
Appeared in Discrete and Computational Geometry 59 (2018), no. 3, 621 – 642.
A preprint is available at the arXiv.
Hao Chen and Arnau Padrol
Scribability problems for polytopes
Appeared in the European Journal of Combinatorics 64 (2017), 1 – 26.
A preprint is available at the arXiv.
An extended abstract appeared in Proc. XVI Spanish Meeting on Computational Geometry , Barcelona 2015, pp. 97–100.
Karim A. Adiprasito and Arnau Padrol
The universality theorem for neighborly polytopes
Appeared in Combinatorica 37 (2017), no. 2, 129–136.
A preprint is available at the arXiv.
Arnau Padrol
Extension complexity of polytopes with few vertices or facets
Appeared in SIAM Journal on Discrete Mathematics, 30 (2016), no. 4, pp. 2162–2176.
A preprint is available at the arXiv.
Arnau Padrol and Günter M. Ziegler
Six topics on inscribable polytopes
Appeared in Advances in Discrete Differential Geometry, (2016) pp. 407–419.
A preprint is available at the arXiv.
Arnau Padrol
Polytopes with few vertices and few facets
Appeared in the Journal of Combinatorial Theory, Series A 142 (2016), pp. 177–180.
A preprint is available at the arXiv.
Bernd Gonska and Arnau Padrol
Neighborly inscribed polytopes and Delaunay triangulations
Appeared in Advances in Geometry 16 (2016), no. 3, pp. 349–360.
A preprint is available at the arXiv.
An extended abstract appeared as Many neighborly inscribed polytopes and Delaunay triangulations in DMTCS Proceedings, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014) , 2014, pp. 161-168.
Karim A. Adiprasito and Arnau Padrol
A universality theorem for projectively unique polytopes and a conjecture of Shephard
Appeared in the Israel Journal of Mathematics 211 (2016), no. 1, pp. 239–255.
A preprint is available at the arXiv.
Karim A. Adiprasito, Arnau Padrol and Louis Theran
Universality theorems for inscribed polytopes and Delaunay triangulations
Appeared in Discrete and Computational Geometry 54 (2015), no. 2, pp. 412–431.
A preprint is available at the arXiv.
An extended abstract of a previous version coauthored with Louis Theran appeared as Delaunay triangulations with disconnected realization spaces in Proceedings of the 30th annual symposium on Computational geometry (SOCG 2014) , 2014, pp. 163-170.
Julian Pfeifle and Arnau Padrol
Polygons as sections of higher-dimensional polytopes
Appeared in the Electronic Journal of Combinatorics 22(1) (2015), #P1.24.
A preprint of this article is available on the arXiv.
Cesar Ceballos, Arnau Padrol and Camilo Sarmiento
Dyck path triangulations and extendability
Appeared in the Journal of Combinatorial Theory, Series A 131(0) (2015), 187–208.
A preprint is available at the arXiv.
An extended abstract appeared in DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015) , 2015, pp. 73-84.
Hiroyuki Miyata and Arnau Padrol
Enumerating neighborly polytopes and oriented matroids,
Appeared in Experimental Mathematics 24 (2015), no. 4, pp. 489–505.
A preprint is available at the arXiv. Here is the database.
Benjamin Nill and Arnau Padrol
The degree of point configurations: from Ehrhart theory to almost neighborly polytopes
Appeared in the special issue of the European Journal of Combinatorics in honour of Michel Las Vergnas, Volume 50 (2015), pp. 159–179.
A preprint is available at the arXiv.
An extended abstract of a preliminary version appeared as Polytopes of combinatorial degree 1 in Proc. VIII Jornadas de Matemática Discreta y Algorítmica , Almería, 2012, pp. 13-20.
Arnau Padrol and Victor Muntés Mulero
Graph anonymization via metric embeddings: Using classical anonymization for graphs
Appeared in Intelligent Data Analysis 18(3): 365-388 (2014)
Arnau Padrol
Many neighborly polytopes and oriented matroids
Appeared in Discrete and Computational Geometry 50 (2013), no. 4, pp. 865–902.
A preprint is available at the arXiv.
An extended abstract appeared as Constructing neighborly polytopes and oriented matroids in DMTCS Proceedings, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) , 2012, pp. 203-214.
Antonio Guedes de Oliveira, Edward Kim, Marc Noy, Arnau Padrol, Julian Pfeifle and Vincent Pilaud
Polytopal complexes realizing products of graphs
Appeared in Proc. XIV Encuentros de Geometría Computacional , Alcalá de Henares, June 2011, pp. 161-164.
No journal version is planned.
Arnau Padrol and Julian Pfeifle
Graph Operations and Laplacian Eigenpolytopes
Appeared in Proc. VII Jornadas de Matemática Discreta y Algorítmica , Castro Urdiales, July 2010, pp. 505-516.
No journal version is planned.
Arnau Padrol, Guillem Perarnau, Julian Pfeifle and Victor Muntés Mulero
Overlapping Community Search for Social Networks
Appeared in Proc. 26th IEEE International Conference on Data Engineering (ICDE) , Long Beach, March 2010, pp. 992--995.
An extended abstract appeared in Proc. XIII Encuentros de Geometría Computacional , Zaragoza, 2009, pp. 173-180. (Spanish)
No journal version is planned.

Theses and reports

Some aspects of the geometric combinatorics of convex polytopes
Habilitation à diriger des recherches. Sorbonne Université. 2020.
Neighborly and almost neighborly configurations, and their duals
PhD thesis. 2013. Advised by Julian Pfeifle.
Graph Anonymization via Metric Embeddings
Informatics engineering degree thesis. 2010. Advised by Victor Muntés Mulero.
Overlapping Community Search in Very Large Graphs
MSc thesis. 2009. Advised by Julian Pfeifle and Victor Muntés Mulero.

Supervision

PhD Students

Chiara Mantovani (2022-2025)
Eva Philippe (2021-2024)
Germain Poullot (2020-2023)

Postdocs

Leonardo Martínez-Sandoval (2018-2019). Currenlty at UNAM.

Teaching

2022-2023

Semestre Primavera

Geometria Lineal
Veure el campus virtual

Semestre Tardor

Grafs
Veure el campus virtual
Geometria Lineal
Veure el campus virtual
Àlgebra Lineal (Eng. Química i de Materials)
Veure el campus virtual

2022-2023

Semestre Tardor

Grafs
Veure el campus virtual
Àlgebra Lineal (Eng. Química i de Materials)
Veure el campus virtual

2021-2022 (SU)

2ème semestre

4M038: Combinatoire et optimisation - M1 (TD)
Voir aussi le site de Michel Pocchiola

1er semestre

2MA226: Graphes et combinatoire - L2 (Amphi + FOAD)
Voir le site du cours à moodle
3MA260: Topologie et calcul différentiel - L3 (TD8)
Voir le site du cours à moodle

2020-2021 (SU)

2ème semestre

5MF82: Combinatoire des polytopes - M2 (cours)
Voir la présentation du cours et des informations générales sur le parcours combinatoire
2MA100: Programmation Python pour les mathématiques - L2 (TP 5a)
Voir le site du cours à moodle et le site de Julien Guillod

1er semestre

2M226: Graphes et combinatoire - L2 (Amphi + TD6)
Voir le site du cours à moodle

2019-2020 (SU)

2ème semestre

5MF82: Combinatoire des polytopes - M2 (cours)
Voir la présentation du cours et des informations générales sur le parcours combinatoire

1er semestre

2M226: Graphes et combinatoire - L2 (Amphi)
Voir le site du cours à moodle

2018-2019 (SU)

2ème semestre

5MF82: Combinatoire des polytopes - M2 (cours)
Voir la présentation du cours et des informations générales sur le parcours combinatoire
4M068: Combinatoire et optimisation - M1 (TD)
Voir aussi le site de Michel Pocchiola

1er semestre

2M226: Graphes et combinatoire - L2 (Amphi + TD6)
Voir le site du cours à moodle

2017-2018 (SU)

2ème semestre

4M068: Combinatoire et optimisation - M1 (TD)

1er semestre

2M226: Graphes et combinatoire - L2 (Amphi + TD1)
4M017: Algorithmique et complexité - M1 (TD)
Voir aussi le site de Michel Pocchiola

2016-2017 (SU)

2ème semestre

2M226: Combinatoire et Graphes - L2 (TD)
4M068: Combinatoire et optimisation - M1 (TD)

1er semestre

1M001: Analyse et algèbre pour les sciences - L1 (TD G12.3)
2M270: Algèbre linéaire 2, espaces affines - L2 (TD2)
Voir aussi le site de Vincent Humilière