HELLY TYPE RESULTS
A mélange of diameter Helly-type theorems
Joint with Travis Dillon
Year:
2020
Status:
Accepted in SIAM J. Discrete Math. (SIDMA)
Isometric and affine copies of a set in volumetric Helly results
Joint with John A. Messina
Year:
2020
Status:
Submitted to journal
Quantitative combinatorial geometry for concave functions
Joint with Sherry Sarkar and Alexander Xue
Year:
2019
Status:
Accepted in J. Combin. Theory Ser. A
Quantitative (p, q) theorems in combinatorial geometry
Joint with David Rolnick
Year:
2017
Reference:
Discrete Math. 340 (10) pp.2516–2527
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
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
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.
Helly-type theorems for the diameter
Year:
2016
Reference:
Bull. London Math. Soc. 48 (4): 577-588
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
On a Problem by Dol’nikov.
Joint with Jesús Jerónimo-Castro
Year:
2015
Reference:
Discrete Math. 338(9) pp 1577–1585
Piercing Numbers for Balanced and Unbalanced Families
Joint with Luis Montejano
Year:
2011
Reference:
Discrete Comput. Geom. 45(2), pp.358–364