Tverberg theory

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.

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

Improved Tverberg theorems for certain families of polytopes

Pablo Soberón, Shira Zerbib

Discrete Comput. Geom. (76) pp. 1960-1970

Tverberg Partition Graphs

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

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

Tverberg's theorem and multi-class support vector machines

Pablo Soberón

Found. Data Sci. 7 (2), 568–580.

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.

Combinatorial Depth Measures for Hyperplane Arrangements

Patrick Schnider, Pablo Soberón

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

Counterexamples to the Colorful Tverberg Conjecture for Hyperplanes

João Pedro Carvalho, Pablo Soberón

Acta Mathematica Hungarica 167, 385–392.

Tolerance for colorful Tverberg partitions

Sherry Sarkar, Pablo Soberón

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

Quantitative combinatorial geometry for concave functions

Sherry Sarkar, Alexander Xue, Pablo Soberón

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

Tverberg's theorem, disks, and Hamiltonian cycles

Pablo Soberón, Yaqian Tang

Ann. Comb. 25, 995–1005.

The topological Tverberg problem beyond prime powers

Florian Frick, Pablo Soberón

Tverberg partitions as weak epsilon-nets

Pablo Soberón

Combinatorica 39 (2), 447–458.

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.

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.

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.

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.

Equal coefficients and tolerance in coloured Tverberg partitions

Pablo Soberón

Combinatorica 35 (2), 235–252.

A Generalisation of Tverberg’s Theorem

Pablo Soberón, Ricardo Strausz

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