Research

TVERBERG TYPE RESULTS

tverberg.png

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

Counterexamples to the Colorful Tverberg Conjecture for Hyperplanes

Joint with João Pedro Carvalho

Year

2021

Status:

Submitted to journal

arXiv version

Tolerance for colorful Tverberg partitions

Joint with Sherry Sarkar

Year:

2020

Status:

Submitted to journal

arXiv version

The topological Tverberg problem beyond prime powers

Joint with Florian Frick

Year:

2020

Status:

Submitted to journal

arXiv version

Tverberg's theorem, disks, and Hamiltonian cycles

Joint with Yaqian Tang

Year:

2020

Status:

Accepted in Ann. Comb.

arXiv version

Tverberg partitions as weak epsilon-nets

​

Year:

2019

Reference:

Combinatorica 39 (2) pp 447–458.

arXiv version

Tverberg plus minus

Joint with Imre Bárány

Year:

2018

Reference:

Discrete Comput. Geom. 60 (3) pp.588–598

arXiv version

Robust Tverberg and colorful Carathéodory results via random choice

​

Year:

2018

Reference:

Combinatorics, Probability and Computing. 27 (3) pp.427–440

arXiv version

Tverberg’s theorem is 50 years old: a survey

Joint with Imre Bárány

Year:

2018

Reference:

Bull. Amer. Math. Soc. 55 (4) pp.459–492

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

Tensors, colors, and convex hulls

​

Year:

2017

Reference:

Discrete Geometry and Convexity: in honour of Imre B ́ar ́any. Edited by Gergely Ambrus, K ́aroly J. B ̈or ̈oczky and Zolt ́an Fu ̈redi. pp.97–101
ISBN 978 963 279 963 6

No arXiv version

Quantitative Tverberg theorems over lattices and other discrete sets

Joint with Jesús de Loera, Reuben La Haye, and David Rolnick

Year:

2017

Reference:

Discrete Comput. Geom. 58 (2) pp.435–458

arXiv version

Helly-type theorems for the diameter

​

Year:

2016

Reference:

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

arXiv version

Algorithms for Tverberg's theorem via centerpoint theorems

Joint with David Rolnick

Year:

2016

Status:

---

arXiv version

Equal coefficients and tolerance in coloured Tverberg partitions

​

Year:

2015

Reference:

Combinatorica 35(2) pp. 235-252

arXiv version

A Generalisation of Tverberg’s Theorem

Joint with Ricardo Strausz

Year:

2012

Reference:

Discrete Comput. Geom. 47(3), pp.455-460

no arXiv version