### Preprints

Gromov−Hausdorff distances, Borsuk−Ulam theorems, and Vietoris−Rips complexes

with Henry Adams, Johnathan Bush, Nate Clause, Mario Gómez, Michael Harrison, R. Amzi Jeffs, Evgeniya Lagoda, Sunhyuk Lim, Facundo Mémoli, Michael Moy, Nikola Sadovek, Matt Superdock, Daniel Vargas, Qingsong Wang, Ling Zhou

Preprint, 33 pages

Transversal generalizations of hyperplane equipartitions

with Samuel Murray, Steven Simon, and Laura Stemmler

Preprint, 24 pages

Unit sphere fibrations in Euclidean space

with Daniel Asimov, Michael Harrison, and Wesley Pegden

Preprint, 11 pages

Colorful Words and d-Tverberg Complexes

with R. Amzi Jeffs

Preprint, 11 pages

Vertex numbers of simplicial complexes with free abelian fundamental group

with Matt Superdock

Preprint, 13 pages

The topological Tverberg problem beyond prime powers

with Pablo Soberón

Preprint, 13 pages

The geometry of fair division

submitted to *Snapshots of modern mathematics from Oberwolfach*

On affine Tverberg-type results without continuous generalization

Preprint, 13 pages

### Journal Publications

On inscribed trapezoids and affinely 3-regular maps

with Michael Harrison

*Proc. Roy. Soc. Edinburgh Sect. A*, to appear

Random complexes with free involution

with Andrew Newman

*Israel. J. Math.*, to appear

Embedding dimensions of simplicial complexes on few vertices

with Mirabel Hu, Verity Scheel, and Steven Simon

*Ann. Comb.*, to appear

Vietoris thickenings and complexes have isomorphic homotopy groups

with Henry Adams and Žiga Virk

*J. Appl. Comput. Topol.*, to appear

The topology of projective codes and the distribution of zeros of odd maps

with Henry Adams and Johnathan Bush

*Michigan Math. J.*, to appear

Coupled embeddability

with Michael Harrison

*Bull. London Math. Soc.* **54** (5), 1609−1629 (2022)

What can you draw?

with Fei Peng

*Amer. Math. Monthly*, to appear

A nonlinear Lazarev−Lieb theorem: L^{2}-orthogonality via motion planning

with Matt Superdock

*J. Topol. Anal.* **14** (3), 569−585 (2022)

Spaces of embeddings: Nonsingular bilinear maps, chirality, and their generalizations

with Michael Harrison

*Proc. Amer. Math. Soc.* **150**, 423−437 (2022)

Barycenters of points in polytope skeleta

with Michael Gene Dobbins

*Contemp. Math.* **764**, 83−88 (2021)

Borsuk−Ulam theorems for products of spheres and Stiefel manifolds revisited

with Yu Hin Chan, Shujian Chen, and J. Tristan Hull

*Topol. Methods Nonlinear Anal.* **55** (2), 553−564 (2020)

Fair splittings by independent sets in sparse graphs

with Alexander Black, Umur Cetin, Alexander Pacun, and Linus Setiabrata

*Israel J. Math.* **236**, 603−627 (2020)

arXiv version

Chromatic numbers of stable Kneser hypergraphs via topological Tverberg-type theorems

*Int. Math. Res. Not. IMRN* **2020** (13), 4037−4061 (2020)

arXiv version

Splitting loops and necklaces: Variants of the square peg problem

with Jai Aslam, Shujian Chen, Sam Saloff-Coste, Linus Setiabrata, and Hugh Thomas

*Forum Math. Sigma* **8**, e5 (2020)

Metric thickenings, Borsuk−Ulam theorems, and orbitopes

with Henry Adams and Johnathan Bush

*Mathematika* **66**, 79−102 (2020)

Colorful coverings of polytopes and piercing numbers of colorful d-intervals

with Shira Zerbib

*Combinatorica* **39** (3), 627−637 (2019)

arXiv version

Barycenters of Polytope Skeleta and Counterexamples to the Topological Tverberg Conjecture, via Constraints

with Pavle Blagojević and Günter M. Ziegler

*J. Europ. Math. Soc. (JEMS)* **21** (7), 2107−2116 (2019)

arXiv version

Neural codes, decidability, and a new local obstruction to convexity

with Aaron Chen and Anne Shiu

*SIAM J. Appl. Algebra Geom.* **3** (1), 44−66 (2019)

arXiv version

Achieving rental harmony with a secretive roommate

with Kelsey Houston-Edwards and Frédéric Meunier

*Amer. Math. Monthly* **126** (1), 18−32 (2019)

arXiv version

On the generalized Erdős−Kneser conjecture: Proofs and reductions

with Jai Aslam, Shuli Chen, Ethan Coldren, and Linus Setiabrata

*J. Combin. Theory, Ser. B* **135**, 227−237 (2019)

arXiv version

Metric reconstruction via optimal transport

with Michal Adamaszek and Henry Adams

*SIAM J. Appl. Algebra Geom.* **2** (4), 597−619 (2018)

arXiv version

Topology of the Grünbaum−Hadwiger−Ramos hyperplane mass partition problem

with Pavle Blagojević, Albert Haase, and Günter M. Ziegler

*Trans. Amer. Math. Soc.* **370** (10), 6795−6824 (2018)

arXiv version

On Reay's relaxed Tverberg conjecture and generalizations of Conway's thrackle conjecture

with Megumi Asada, Ryan Chen, Frederick Huang, Maxwell Polevy, David Stoner, Ling Hei Tsang, and Zoe Wellner

*Electronic J. Combin.* **25** (3), P3.16, 14 pages (2018)

arXiv version

Fair division and generalizations of Sperner- and KKM-type results

with Megumi Asada, Vivek Pisharody, Maxwell Polevy, David Stoner, Ling Hei Tsang, and Zoe Wellner

*SIAM J. Discrete Math.* **32** (1), 591−610 (2018)

arXiv version

On homotopy types of Euclidean Rips complexes

with Michal Adamaszek and Adrien Vakili

*Discrete Comput. Geom.* **58** (3), 526−542 (2017)

arXiv version

Minkowski complexes and convex threshold dimension

with Raman Sanyal

*J. Combin. Theory, Ser. A* **151**, 202−206 (2017)

arXiv version

Intersection patterns of finite sets and of convex sets

*Proc. Amer. Math. Soc.* **145** (7), 2827−2842 (2017)

arXiv version

Hyperplane mass partitions via relative equivariant obstruction theory

with Pavle Blagojević, Albert Haase, and Günter M. Ziegler

*Documenta Math.* **21**, 735−771 (2016)

arXiv version

Nerve complexes of circular arcs

with Michal Adamaszek, Henry Adams, Chris Peterson, and Corrine Previte-Johnson

*Discrete Comput. Geom.* **56** (2), 251−273 (2016)

arXiv version

Tverberg plus constraints

with Pavle Blagojević and Günter M. Ziegler

*Bull. London Math. Soc.* **46**, 953−967 (2014)

arXiv version

### Proceedings and non-refereed publications

The topological Tverberg problem beyond prime powers

Report on results in the the paper by the same title with Pablo Soberón

*Oberwolfach Reports*, to appear

Generalizations of the Borsuk−Ulam Theorem

Report on some results in "Metric thickenings, Borsuk−Ulam theorems, and orbitopes" with Henry Adams and Johnathan Bush

*Oberwolfach Reports* (Kalai Gil, Novik Isabella, Santos Francisco, Welker Volkmar, eds.): Geometric, Algebraic, and Topological Combinatorics. Oberwolfach Rep. 16 (2019), 2395-2472. doi: 10.4171/OWR/2019/39

A Pearl in Combinatorial Convexity — Tverberg's Theorem

with Imre Bárány

*Emissary* Fall 2017, 1 & 11−12

lead article for the *Geometric and Topological Combinatorics* program at MSRI

Counterexamples to the topological Tverberg conjecture

*Oberwolfach Reports* **12**(1) (2015), 318−321

Oberwolfach Reports **12**(1)

A minimal irreducible triangulation of S^{3}

*Proc. Combinatorial Methods in Topology and Algebra*

Editors: B. Benedetti, E. Delucchi, L. Moci

Volume 12 (2015) of the series Springer INdAM Series pp 49−52

### Dissertation

Combinatorial restrictions on cell complexes

June 2015, Technische Universität Berlin

Advisor: John M. Sullivan

Referee: Imre Bárány

### Miscellaneous

Barycenters of points that are constrained to a polytope skeleton

with Pavle Blagojević and Günter M. Ziegler

2 pages, not for publication

subsumed by "Barycenters of Polytope Skeleta and Counterexamples to the Topological Tverberg Conjecture, via Constraints"