Vietoris thickenings and complexes have isomorphic homotopy groups
with Henry Adams and Žiga Virk
Preprint, 14 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

On inscribed trapezoids and affinely 3-regular maps
with Michael Harrison
Preprint, 4 pages, submitted

Embedding dimensions of simplicial complexes on few vertices
with Mirabel Hu, Nick Scheel, and Steven Simon
Preprint, 5 pages, submitted

The topological Tverberg problem beyond prime powers
with Pablo Soberón
Preprint, 13 pages, submitted

The geometry of fair division
submitted to Snapshots of modern mathematics from Oberwolfach

On affine Tverberg-type results without continuous generalization
Preprint, 13 pages, submitted

Journal Publications

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., to appear

What can you draw?
with Fei Peng
Amer. Math. Monthly, to appear

A nonlinear Lazarev−Lieb theorem: L2-orthogonality via motion planning
with Matt Superdock
J. Topol. Anal., to appear

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 S3
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


Combinatorial restrictions on cell complexes
June 2015, Technische Universität Berlin
Advisor: John M. Sullivan
Referee: Imre Bárány


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"