
PAPERS/MANUSCRIPTS
FULL LIST

The topological Tverberg problem beyond prime powers
Joint with Florian Frick
Year:
Status:
2020
Submitted to journal

Tverberg's theorem, disks, and Hamiltonian cycles
Joint with Yaqian Tang
Year:
Status:
2020
Submitted to journal

A survey of mass partitions
Joint with Edgardo Roldán-Pensado
Year:
Status:
2020
Accepted in Bull. Amer. Math. Soc.

Isometric and affine copies of a set in volumetric Helly results
Joint with John A. Messina
Year:
Status:
2020
Submitted to journal

A mélange of diameter Helly-type theorems
Joint with Travis Dillon
Year:
Status:
2020
Submitted to journal

Tolerance for colorful Tverberg partitions
Joint with Sherry Sarkar
Year:
Status:
2020
Submitted to journal

Quantitative combinatorial geometry for concave functions
Joint with Sherry Sarkar and Alexander Xue
Year:
Status:
2019
Accepted in J. Combin. Theory Ser. A

Balanced convex partitions of lines in the plane
Joint with Alexander Xue
Year:
Status:
2019
Accepted in Discrete Comput. Geom.

Tverberg partitions as weak epsilon-nets
Year:
Reference:
2019
Combinatorica 39 (2) pp 447–458.

Prescribing Symmetries and Automorphisms for Polytopes
Joint with Egon Schulte and Gordon I Williams
Year:
Status:
2019
Accepted in Contemporary Mathematics

Cutting a part of many measures
Joint with Pavle V. M. Blagojevic, Nevena Palic, and Günter M. Ziegler
Year:
Reference:
2019
Forum of Mathematics, Sigma 7 E37

Finite groups as prescribed polytopal symmetries
Joint with Alexandru Chirvasitu and Frieder Ladisch
Year:
Status:
2019
Accepted in Israel J. Math.

Robust Tverberg and colorful Carathéodory results via random choice
Year:
Reference:
2018
Combinatorics, Probability and Computing. 27 (3) pp.427–440

Tverberg’s theorem is 50 years old: a survey
Joint with Imre Bárány
Year:
Reference:
2018
Bull. Amer. Math. Soc. 55 (4) pp.459–492

Tverberg plus minus
Joint with Imre Bárány
Year:
Reference:
2018
Discrete Comput. Geom. 60 (3) pp.588–598

Thieves can make sandwiches
Joint with Pavle V. M. Blagojevic
Year:
Reference:
2018
Bull. London Math. Soc. 50 (1) pp.108–123
A Note on the Maximum Rectilinear Crossing Number of Spiders
Joint with Joshua Fallon, Kirsten Hogenson, Lauren Keough, Mario Lomelí, and Marcus Schaefer
Year:
Status:
2018
Accepted at J. Combinatorial Math. and Combinatorial Computing

Computing the Partition Function for Graph Homomorphisms
Joint with Alexander Barvinok
Year:
Reference:
2017
Combinatorica 37 (4) pp.633–650.

Quantitative (p, q) theorems in combinatorial geometry
Joint with David Rolnick
Year:
Reference:
2017
Discrete Math. 340 (10) pp.2516–2527

Quantitative Tverberg theorems over lattices and other discrete sets
Joint with Jesús de Loera, Reuben La Haye, and David Rolnick
Year:
Reference:
2017
Discrete Comput. Geom. 58 (2) pp.435–458

Tensors, colors, and convex hulls
Year:
Reference:
2017
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
Helly’s Theorem: New Variations and Applications
Joint with Jesús de Loera and Nina Amenta
Year:
Reference:
2017
“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:
Reference:
2017
Discrete Comput. Geom. 57(2) pp.318–334
Positive-fraction intersection results and variations of weak epsilon-nets
Joint with Alexander Magazinov
Year:
Reference:
2017
Monatshefte für Mathematik. 183 (1) pp.165–176.
Algorithms for Tverberg's theorem via centerpoint theorems
Joint with David Rolnick
Year:
Status:
2016
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Helly-type theorems for the diameter
Year:
Reference:
2016
Bull. London Math. Soc. 48 (4): 577-588
Computing the Partition Function for Graph Homomorphisms with Multiplicities
Joint with Alexander Barvinok
Year:
Reference:
2016
J. Combin. Theory, Ser. A 137 pp. 1–26
Measure Partitions Using Hyperplanes with Fixed
Directions
Joint with Roman Karasev and Edgardo Roldán-Pensado
Year:
Reference:
2016
Israel J. Math. 212(2) pp 705–708
About an Erdős-Grünbaum conjecture
concerning piercing of non bounded convex sets
Joint with Amanda Montejano, Luis Montejano, and Edgardo Roldán-Pensado
Year:
Reference:
2015
Discrete Comput. Geom. 53(4) pp 941–950
On a Problem by Dol’nikov.
Joint with Jesús Jerónimo-Castro
Year:
Reference:
2015
Discrete Math. 338(9) pp 1577–1585
Equal coefficients and tolerance in coloured Tverberg partitions
Year:
Reference:
2015
Combinatorica 35(2) pp. 235-252
An Extension of a Theorem by Yao & Yao
Joint with Edgardo Roldán-Pensado
Year:
Reference:
2014
Discrete Comput. Geom.
51(2), pp.285-289
Balanced Convex Partitions of Measures in R^d
Year:
Reference:
2012
Mathematika 58, pp.71-76
A Generalisation of Tverberg’s Theorem
Joint with Ricardo Strausz
Year:
Reference:
2012
Discrete Comput. Geom. 47(3), pp.455-460
Piercing Numbers for Balanced and Unbalanced Families
Joint with Luis Montejano
Year:
Reference:
2011
Discrete Comput. Geom. 45(2), pp.358–364