top of page

FULL LIST OF PAPERS

Fair distribution of bundles

​

Year:

2025

Status:

​

arXiv version

Cookie cutters: Bisections with fixed shapes

Joint with Patrick Schnider

Year:

2025

Status:

Submitted for publication

arXiv version

Partitions of mass assignments with spheres and wedges

Joint with Deron Lessure

Year:

2025

Status:

​

arXiv version

Tverberg Partition Graphs

Joint with Deborah Oliveros, Érika Roldán, and Antonio J. Torres

Year:

2025

Status:

SIAM J. Discrete Math. 39 (2), 863-880

arXiv version

Extensions of discrete Helly theorems for boxes

Joint with Timothy Edwards

Year:

2025

Status:

SIAM J. Discrete Math. 39 (2), 1349-1362

arXiv version

Tverberg's theorem and multi-class support vector machines

​

Year:

2025

Status:

Found. Data Sci. 7(2) pp. 568-580

arXiv version

Complex analogues of the Tverberg--Vre\'cica conjecture and central transversal theorems

Joint with Nikola Sadovek

Year:

2024

Accepted to Trans. Amer. Math. Soc.

Accepted to Trans. Amer. Math. Soc.

arXiv version

Bisections of mass assignments by parallel hyperplanes

Joint with Nikola Sadovek

Year:

2024

Status:

​

arXiv version

Bisecting masses with families of parallel hyperplanes

Joint with Alfredo Hubard

Year:

2024

Status

Submitted for publication

arXiv version

Generalizations of the Yao-Yao partition theorem and the central transversal theorem

Joint with Michael N. Manta

Year:

2024

Status:

Discrete Comput. Geom. 71 (4), 1381-1402

arXiv version

Improved Tverberg theorems for certain families of polytopes

Joint with Shira Zerbib

Year:

2024

Status:

Submitted for Publication

arXiv version

Bisections of mass assignments using flags of affine spaces

Joint with Ilani Axelrod-Freed

Year:

2024

Status:

Discrete Comput. Geom. 72 (2), 550-568

arXiv version

Combinatorial Depth Measures for Hyperplane Arrangements

Joint with Patrick Schnider

Year:

2023

Status:

39th International Symposium on Computational Geometry, Art. No. 55, 14 pp., LIPIcs. Leibniz Int. Proc. Inform., 258, Schloss Dagstuhl. Leibniz-Zent.

arXiv version

Colorful and Quantitative Variations of Krasnosselsky's Theorem

Joint with Connor Donovan and Danielle Paulson

Year:

2023

Status:

Accepted to Studia Scientiarum Mathematicarum Hungarica

arXiv version

High-dimensional envy-free partitions

Joint with Christina Yu

Year:

2023

Status:

Submitted for Publication

arXiv version

Lifting methods in mass partition problems

Joint with Yuki Takahashi

Year:

2023

Reference:

Int. Math. Res. Not. IMRN, 2023 (16), pp. 14103-14130

arXiv version

Fair distributions for more participants than allocations

​

Year:

2022

Reference:

Proc. Amer. Math. Soc., Ser. B 9 pp. 404–414

arXiv version

Counterexamples to the Colorful Tverberg Conjecture for Hyperplanes

Joint with João Pedro Carvalho

Year

2022

Reference

Acta Mathematica Hungarica 167, 385–392

arXiv version

A survey of mass partitions

Joint with Edgardo Roldán-Pensado

Year:

2022

Reference:

Bull. Amer. Math. Soc. 59(2) pp. 227-267

arXiv version

Tolerance for colorful Tverberg partitions

Joint with Sherry Sarkar

Year:

2022

Reference:

European J. Combin 103, paper 103527

arXiv version

Isometric and affine copies of a set in volumetric Helly results

Joint with John A. Messina

Year:

2022

Reference:

Comput. Geom. 103 101855

arXiv version

Tverberg's theorem, disks, and Hamiltonian cycles

Joint with Yaqian Tang

Year:

2021

Reference:

Ann. Comb. 25 pp 995-1005

arXiv version

Balanced convex partitions of lines in the plane

Joint with Alexander Xue

Year:

2021

Reference:

Discrete Comput. Geom. 66(3), pp 1150-1167

arXiv version

Finite groups as prescribed polytopal symmetries

Joint with Alexandru Chirvasitu and Frieder Ladisch

Year:

2021

Reference:

Israel J. Math. 245(1), 75-91

arXiv version

A mélange of diameter Helly-type theorems

Joint with Travis Dillon

Year:

2021

Reference:

SIAM J. Discrete Math. 35 (3) pp. 1615-1627

arXiv version

Quantitative combinatorial geometry for concave functions

Joint with Sherry Sarkar and Alexander Xue

Year:

2021

Reference:

J. Combin. Theory Ser. A 182 Article 105465

arXiv version

Prescribing Symmetries and Automorphisms for Polytopes

Joint with Egon Schulte and Gordon I Williams

Year:

2021

Reference:

Polytopes and Discrete Geometry, Contemporary Mathematics 764, Amercan Mathematical Society pp221-233

arXiv version

The topological Tverberg problem beyond prime powers

Joint with Florian Frick

Year:

2020

Status:

​

arXiv version

A Note on the Maximum Rectilinear Crossing Number of Spiders

Joint with Joshua Fallon, Kirsten Hogenson, Lauren Keough, Mario Lomelí, and Marcus Schaefer

Year:

2020

Reference:

J. Combin. Math. Combin. Comput. 113 pp. 127-139

arXiv version

Tverberg partitions as weak epsilon-nets

​

Year:

2019

Reference:

Combinatorica 39 (2) pp 447–458.

arXiv version

Cutting a part of many measures

Joint with Pavle V. M. Blagojevic, Nevena Palic, and Günter M. Ziegler

Year:

2019

Reference:

Forum of Mathematics, Sigma 7 E37

arXiv version

Robust Tverberg and colorful Carathéodory results via random choice

​

Year:

2018

Reference:

Combinatorics, Probability and Computing. 27 (3) pp.427–440

arXiv version

Tverberg’s theorem is 50 years old: a survey

Joint with Imre Bárány

Year:

2018

Reference:

Bull. Amer. Math. Soc. 55 (4) pp.459–492

arXiv version

Tverberg plus minus

Joint with Imre Bárány

Year:

2018

Reference:

Discrete Comput. Geom. 60 (3) pp.588–598

arXiv version

Thieves can make sandwiches

Joint with Pavle V. M. Blagojevic

Year:

2018

Reference:

Bull. London Math. Soc. 50 (1) pp.108–123

arXiv version

Computing the Partition Function for Graph Homomorphisms

Joint with Alexander Barvinok

Year:

2017

Reference:

Combinatorica 37 (4) pp.633–650.

arXiv version

Quantitative (p, q) theorems in combinatorial geometry

Joint with David Rolnick

Year:

2017

Reference:

Discrete Math. 340 (10) pp.2516–2527

arXiv version

Quantitative Tverberg theorems over lattices and other discrete sets

Joint with Jesús de Loera, Reuben La Haye, and David Rolnick

Year:

2017

Reference:

Discrete Comput. Geom. 58 (2) pp.435–458

arXiv version

Tensors, colors, and convex hulls

​

Year:

2017

Reference:

Discrete Geometry and Convexity: in honour of Imre B ́ar ́any. Edited by Gergely Ambrus, K ́aroly J. B ̈or ̈oczky and Zolt ́an Fu ̈redi. pp.97–101
ISBN 978 963 279 963 6

arXiv version

Helly’s Theorem: New Variations and Applications

Joint with Jesús de Loera and Nina Amenta

Year:

2017

Reference:

“Algebraic and Geometric Methods in Discrete Mathematics: AMS Special session on Alge-
braic and Geometric Methods in Applied Discrete Mathematics”, Contemporary Math. 685, published
by American Math. Soc., edited by Heather A. Harrington, Mohamed Omar and Matthew Wright. pp.
55-95

arXiv version

Quantitative combinatorial geometry for
continuous parameters

Joint with Jesús de Loera, Reuben La Haye, and David Rolnick

Year:

2017

Reference:

Discrete Comput. Geom. 57(2) pp.318–334

arXiv version

Positive-fraction intersection results and variations of weak epsilon-nets

Joint with Alexander Magazinov

Year:

2017

Reference:

Monatshefte für Mathematik. 183 (1) pp.165–176.

arXiv version

Algorithms for Tverberg's theorem via centerpoint theorems

Joint with David Rolnick

Year:

2016

Status:

---

arXiv version

Helly-type theorems for the diameter

​

Year:

2016

Reference:

Bull. London Math. Soc. 48 (4): 577-588

arXiv version

Computing the Partition Function for Graph Homomorphisms with Multiplicities

Joint with Alexander Barvinok

Year:

2016

Reference:

J. Combin. Theory, Ser. A 137 pp. 1–26

arXiv version

Measure Partitions Using Hyperplanes with Fixed
Directions

Joint with Roman Karasev and Edgardo Roldán-Pensado

Year:

2016

Reference:

Israel J. Math. 212(2) pp 705–708

arXiv version

About an Erdős-Grünbaum conjecture
concerning piercing of non bounded convex sets

Joint with Amanda Montejano, Luis Montejano, and Edgardo Roldán-Pensado

Year:

2015

Reference:

Discrete Comput. Geom. 53(4) pp 941–950

arXiv version

On a Problem by Dol’nikov.

Joint with Jesús Jerónimo-Castro

Year:

2015

Reference:

Discrete Math. 338(9) pp 1577–1585

arXiv version

Equal coefficients and tolerance in coloured Tverberg partitions

​

Year:

2015

Reference:

Combinatorica 35(2) pp. 235-252

arXiv version

An Extension of a Theorem by Yao & Yao

Joint with Edgardo Roldán-Pensado

Year:

2014

Reference:

Discrete Comput. Geom.
51(2), pp.285-289

arXiv version

Balanced Convex Partitions of Measures in R^d

​

Year:

2012

Reference:

Mathematika 58, pp.71-76

arXiv version

A Generalisation of Tverberg’s Theorem

Joint with Ricardo Strausz

Year:

2012

Reference:

Discrete Comput. Geom. 47(3), pp.455-460

arXiv version

Piercing Numbers for Balanced and Unbalanced Families

Joint with Luis Montejano

Year:

2011

Reference:

Discrete Comput. Geom. 45(2), pp.358–364

arXiv version

© 2023 by Pablo Soberón.

bottom of page