2026
preprint
Helly and Radon theorems for convex intersections containing k-flats
Colorful and fractional intersection theorems for convex families whose intersection contains an affine k-flat.
17 papers
Helly-type theorems
How local intersection conditions force global conclusions. Colorful, fractional, and quantitative forms of Helly’s theorem.
2026
submitted
KKM theorems and discrete geometry beyond matroids
Selection structures extend the role of color classes and matroids in KKM theorems and discrete geometry.
2026
2025
published
Colorful and Quantitative Variations of Krasnosselsky's Theorem
Studia Sci. Math. Hungar. 62 (2025), no. 4, 336–353.
2025
2022
published
Isometric and affine copies of a set in volumetric Helly results
Comput. Geom. 103, Paper No. 101855.
2021
published
Quantitative combinatorial geometry for concave functions
J. Combin. Theory Ser. A 182, Article 105465.
2021
2017
2017
published
Quantitative Tverberg theorems over lattices and other discrete sets
Discrete Comput. Geom. 58 (2), 435–458.
2017
published · Survey
Helly’s Theorem: New Variations and Applications
Algebraic and Geometric Methods in Discrete Mathematics, Contemporary Mathematics 685, American Mathematical Society, 55–95.
2017
published
Quantitative combinatorial geometry for continuous parameters
Discrete Comput. Geom. 57 (2), 318–334.
2017
published
Positive-fraction intersection results and variations of weak epsilon-nets
Monatshefte für Mathematik 183 (1), 165–176.
2016
2015
published
About an Erdős–Grünbaum conjecture concerning piercing of non bounded convex sets
Discrete Comput. Geom. 53 (4), 941–950.
2015
2011
published
Piercing Numbers for Balanced and Unbalanced Families
Discrete Comput. Geom. 45 (2), 358–364.