Publications

The topological Bárány–Larman conjecture for prime numbers

Pablo Soberón

The topological Bárány–Larman conjecture for prime numbers, and counterexamples to extending the optimal colorful Tverberg theorem to prime powers.

Discrepancy theory, Tverberg's theorem, and regression depth

Aleksey Lopez, Pablo Soberón

Discrepancy-theoretic bounds for Tverberg partitions with tolerance, for point sets and for regression hulls of hyperplanes.

Helly and Radon theorems for convex intersections containing k-flats

Sarah Ludwigson, Pablo Soberón

Colorful and fractional intersection theorems for convex families whose intersection contains an affine k-flat.

Four hyperplanes do not always equipartition a mass in ℝ⁴

Pablo Soberón

A smooth positive density in four dimensions that admits no equipartition into sixteen equal parts by four affine hyperplanes.

Blocking codimension-one simplices on the moment curve

Pablo Soberón

Selection-structure generalizations of the Borsuk–Ulam theorem

Pablo Soberón

KKM theorems and discrete geometry beyond matroids

Pablo Soberón

Selection structures extend the role of color classes and matroids in KKM theorems and discrete geometry.

Variations of Helly's theorem for convex splinters

Pablo Soberón, Iris Ye

Tverberg cores and Kalai’s cascade conjecture

Pablo Soberón

Topological Tverberg cores, vertex-deletion tolerance, and consequences for Kalai’s cascade conjecture.

An elementary proof of Sierksma's conjecture for seven points in the plane

Pablo Soberón

High-dimensional envy-free partitions

Christina Yu, Pablo Soberón

Comb. Theory 6, no. 1, Paper No. 11, 19 pp.

Fair distribution of bundles

Pablo Soberón

Proc. Amer. Math. Soc. 154, no. 7, 3085–3097.

Partitions of mass assignments with spheres and wedges

Deron Lessure, Pablo Soberón

Accepted in European Journal of Combinatorics

Colorful and Quantitative Variations of Krasnosselsky's Theorem

Connor Donovan, Danielle Paulson, Pablo Soberón

Studia Sci. Math. Hungar. 62 (2025), no. 4, 336–353.

Tverberg Partition Graphs

Deborah Oliveros, Érika Roldán, Pablo Soberón, Antonio J. Torres

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

Extensions of discrete Helly theorems for boxes

Timothy Edwards, Pablo Soberón

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

Tverberg's theorem and multi-class support vector machines

Pablo Soberón

Found. Data Sci. 7 (2), 568–580.

Cookie cutters: Bisections with fixed shapes

Patrick Schnider, Pablo Soberón

Adv. in Appl. Math. 171, Paper No. 102957, 15 pp.

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

Michael N. Manta, Pablo Soberón

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

Bisections of mass assignments using flags of affine spaces

Ilani Axelrod-Freed, Pablo Soberón

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

Improved Tverberg theorems for certain families of polytopes

Pablo Soberón, Shira Zerbib

Accepted to Discrete Comput. Geom.

Bisections of mass assignments by parallel hyperplanes

Nikola Sadovek, Pablo Soberón

Complex analogues of the Tverberg–Vrećica conjecture and central transversal theorems

Nikola Sadovek, Pablo Soberón

Trans. Amer. Math. Soc. 379 (2026), no. 5, 3665–3691.

Bisecting masses with families of parallel hyperplanes

Alfredo Hubard, Pablo Soberón

Combinatorial Depth Measures for Hyperplane Arrangements

Patrick Schnider, Pablo Soberón

39th International Symposium on Computational Geometry, Art. No. 55, 14 pp., LIPIcs 258.

Lifting methods in mass partition problems

Pablo Soberón, Yuki Takahashi

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

Fair distributions for more participants than allocations

Pablo Soberón

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

Counterexamples to the Colorful Tverberg Conjecture for Hyperplanes

João Pedro Carvalho, Pablo Soberón

Acta Mathematica Hungarica 167, 385–392.

A survey of mass partitions

Edgardo Roldán-Pensado, Pablo Soberón

Bull. Amer. Math. Soc. 59 (2), 227–267.

Tolerance for colorful Tverberg partitions

Sherry Sarkar, Pablo Soberón

European J. Combin. 103, Paper No. 103527.

Isometric and affine copies of a set in volumetric Helly results

John A. Messina, Pablo Soberón

Comput. Geom. 103, Paper No. 101855.

Quantitative combinatorial geometry for concave functions

Sherry Sarkar, Alexander Xue, Pablo Soberón

J. Combin. Theory Ser. A 182, Article 105465.

Balanced convex partitions of lines in the plane

Alexander Xue, Pablo Soberón

Discrete Comput. Geom. 66 (3), 1150–1167.

Tverberg's theorem, disks, and Hamiltonian cycles

Pablo Soberón, Yaqian Tang

Ann. Comb. 25, 995–1005.

Finite groups as prescribed polytopal symmetries

Alexandru Chirvasitu, Frieder Ladisch, Pablo Soberón

Israel J. Math. 245 (1), 75–91.

A mélange of diameter Helly-type theorems

Travis Dillon, Pablo Soberón

SIAM J. Discrete Math. 35 (3), 1615–1627.

Prescribing Symmetries and Automorphisms for Polytopes

Egon Schulte, Pablo Soberón, Gordon Ian Williams

Polytopes and Discrete Geometry, Contemporary Mathematics 764, American Mathematical Society, 221–233.

The topological Tverberg problem beyond prime powers

Florian Frick, Pablo Soberón

A Note on the Maximum Rectilinear Crossing Number of Spiders

Joshua Fallon, Kirsten Hogenson, Lauren Keough, Mario Lomelí, Marcus Schaefer, Pablo Soberón

J. Combin. Math. Combin. Comput. 113, 127–139.

Tverberg partitions as weak epsilon-nets

Pablo Soberón

Combinatorica 39 (2), 447–458.

Cutting a part of many measures

Pavle V. M. Blagojević, Nevena Palić, Pablo Soberón, Günter M. Ziegler

Forum of Mathematics, Sigma 7, E37.

Robust Tverberg and colorful Carathéodory results via random choice

Pablo Soberón

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

Tverberg’s theorem is 50 years old: a survey

Imre Bárány, Pablo Soberón

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

Tverberg plus minus

Imre Bárány, Pablo Soberón

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

Thieves can make sandwiches

Pavle V. M. Blagojević, Pablo Soberón

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

Computing the Partition Function for Graph Homomorphisms

Alexander Barvinok, Pablo Soberón

Combinatorica 37 (4), 633–650.

Quantitative (p, q) theorems in combinatorial geometry

David Rolnick, Pablo Soberón

Discrete Math. 340 (10), 2516–2527.

Quantitative Tverberg theorems over lattices and other discrete sets

Jesús A. De Loera, Reuben N. La Haye, David Rolnick, Pablo Soberón

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

Tensors, colors, and convex hulls

Pablo Soberón

Discrete Geometry and Convexity: in honour of Imre Bárány, edited by Gergely Ambrus, Károly J. Böröczky and Zoltán Füredi, 97–101. ISBN 978 963 279 963 6.

Helly’s Theorem: New Variations and Applications

Nina Amenta, Jesús A. De Loera, Pablo Soberón

Algebraic and Geometric Methods in Discrete Mathematics, Contemporary Mathematics 685, American Mathematical Society, 55–95.

Quantitative combinatorial geometry for continuous parameters

Jesús A. De Loera, Reuben N. La Haye, David Rolnick, Pablo Soberón

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

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

Alexander Magazinov, Pablo Soberón

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

Algorithms for Tverberg's theorem via centerpoint theorems

David Rolnick, Pablo Soberón

Helly-type theorems for the diameter

Pablo Soberón

Bull. London Math. Soc. 48 (4), 577–588.

Computing the Partition Function for Graph Homomorphisms with Multiplicities

Alexander Barvinok, Pablo Soberón

J. Combin. Theory Ser. A 137, 1–26.

Measure Partitions Using Hyperplanes with Fixed Directions

Roman N. Karasev, Edgardo Roldán-Pensado, Pablo Soberón

Israel J. Math. 212 (2), 705–708.

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

Amanda Montejano, Luis Montejano, Edgardo Roldán-Pensado, Pablo Soberón

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

On a Problem by Dol’nikov

Jesús Jerónimo-Castro, Alexander Magazinov, Pablo Soberón

Discrete Math. 338 (9), 1577–1585.

Equal coefficients and tolerance in coloured Tverberg partitions

Pablo Soberón

Combinatorica 35 (2), 235–252.

An Extension of a Theorem by Yao & Yao

Edgardo Roldán-Pensado, Pablo Soberón

Discrete Comput. Geom. 51 (2), 285–289.

Balanced Convex Partitions of Measures in ℝᵈ

Pablo Soberón

Mathematika 58, 71–76.

A Generalisation of Tverberg’s Theorem

Pablo Soberón, Ricardo Strausz

Discrete Comput. Geom. 47 (3), 455–460.

Piercing Numbers for Balanced and Unbalanced Families

Luis Montejano, Pablo Soberón

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