## PAPERS/MANUSCRIPTS

## FULL LIST

###### 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

###### The topological Tverberg problem beyond prime powers

Joint with Florian Frick

Year:

Status:

2020

Submitted to journal

###### Quantitative combinatorial geometry for concave functions

Joint with Sherry Sarkar and Alexander Xue

Year:

Status:

2019

Submitted to journal

###### 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.

###### 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

###### Robust Tverberg and colorful Carathéodory results via random choice

Year:

Reference:

2018

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

###### 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

###### 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

###### Computing the Partition Function for Graph Homomorphisms

Joint with Alexander Barvinok

Year:

Reference:

2017

Combinatorica 37 (4) pp.633–650.

###### 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

###### A Generalisation of Tverberg’s Theorem

Joint with Ricardo Strausz

Year:

Reference:

2012

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

###### Balanced Convex Partitions of Measures in R^d

Year:

Reference:

2012

Mathematika 58, pp.71-76

###### Piercing Numbers for Balanced and Unbalanced Families

Joint with Luis Montejano

Year:

Reference:

2011

Discrete Comput. Geom. 45(2), pp.358–364