Pablo Soberón — papershttps://www.psoberon.com/2026-09-29T12:00:00ZPablo Soberónhttps://www.psoberon.com/papers/barany-larman-primes/The topological Bárány–Larman conjecture for prime numbers2026-09-29T12:00:00ZThe topological Bárány–Larman conjecture for prime numbers, and counterexamples to extending the optimal colorful Tverberg theorem to prime powers.https://www.psoberon.com/papers/discrepancy-tverberg-regression/Discrepancy theory, Tverberg's theorem, and regression depth2026-09-21T12:00:00ZDiscrepancy-theoretic bounds for Tverberg partitions with tolerance, for point sets and for regression hulls of hyperplanes.https://www.psoberon.com/papers/helly-radon-flats/Helly and Radon theorems for convex intersections containing k-flats2026-08-27T12:00:00ZColorful and fractional intersection theorems for convex families whose intersection contains an affine k-flat.https://www.psoberon.com/papers/four-hyperplanes/Four hyperplanes do not always equipartition a mass in ℝ⁴2026-08-24T12:00:00ZA smooth positive density in four dimensions that admits no equipartition into sixteen equal parts by four affine hyperplanes.https://www.psoberon.com/papers/beyond-matroids/KKM theorems and discrete geometry beyond matroids2026-06-15T12:00:00ZSelection structures extend the role of color classes and matroids in KKM theorems and discrete geometry.https://www.psoberon.com/papers/tverberg-cores/Tverberg cores and Kalai’s cascade conjecture2026-05-20T12:00:00ZTopological Tverberg cores, vertex-deletion tolerance, and consequences for Kalai’s cascade conjecture.