Helly type results

Research

HELLY TYPE RESULTS

Extensions of discrete Helly theorems for boxes

Joint with Timothy Edwards

Year:

2024

Status:

arXiv version

Colorful and Quantitative Variations of Krasnosselsky's Theorem

Joint with Connor Donovan and Danielle Paulson

Year:

2023

Status:

Submitted to journal

arXiv version

Combinatorial Depth Measures for Hyperplane Arrangements

Joint with Patrick Schnider

Year:

2023

Status:

Accepted to SoCG 2023

arXiv version

Isometric and affine copies of a set in volumetric Helly results

Joint with John A. Messina

Year:

2022

Reference:

Comput. Geom. 103 101855

arXiv version

A mélange of diameter Helly-type theorems

Joint with Travis Dillon

Year:

2021

Reference:

SIAM J. Discrete Math. 35 (3) pp. 1615-1627

arXiv version

Quantitative combinatorial geometry for concave functions

Joint with Sherry Sarkar and Alexander Xue

Year:

2021

Reference:

J. Combin. Theory Ser. A 182 Article 105465

arXiv version

Quantitative (p, q) theorems in combinatorial geometry

Joint with David Rolnick

Year:

2017

Reference:

Discrete Math. 340 (10) pp.2516–2527

arXiv version

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

arXiv version

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

arXiv version

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.

arXiv version

Helly-type theorems for the diameter

Year:

2016

Reference:

Bull. London Math. Soc. 48 (4): 577-588

arXiv version

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

arXiv version