Publications

A Z₂-Topological Framework for Sign-rank Lower Bounds

with Kaave Hosseini and Aliaksei Vasileuski

Preprint.

arXiv 2604.01510

An optimal Brouwer’s fixed point theorem for discontinuous functions

with Henry Adams

Preprint.

arXiv 2512.14934

Quantifying discontinuity

with Henry Adams, Michael Harrison, Nikola Sadovek, and Matt Superdock

Preprint.

arXiv 2511.07636

Covering and labeling generalizations of the Borsuk–Ulam theorem

with Zoe Wellner

Preprint.

arXiv 2509.07247

Geodesic complexity of the octahedron, and an algorithm for cut loci on convex polyhedra

with Pranav Rajbhandari

Preprint.

arXiv 2508.19362

Roots of real-valued zero mean maps: Compositions of linear functionals and equivariant maps

with Francesca Cantor, Julia D’Amico, and Eric Myzelev

Europ. J. Math. 12, 1 (2026).

arXiv 2503.19729

Youden’s Demon is Sylvester’s Problem

with Andrew Newman and Wesley Pegden

Mathematika 71 (2), e70015 (2025).

arXiv 2407.02589

Appendix to D. Kozlov, “Homology and Euler characteristic of generalized anchored configuration spaces of graphs”

with Martin Raussen

J. Appl. Comput. Topol. 8, 1053–1067 (2024).

DOI 10.1007/s41468-024-00167-8

Topological methods in zero-sum Ramsey theory

with Jacob Lehmann Duke, Meenakshi McNamara, Hannah Park-Kaufmann, Steven Raanes, Steven Simon, Darrion Thornburgh, and Zoe Wellner

Forum Math. Sigma 13, e192 (2025).

arXiv 2310.17065

Hausdorff vs Gromov–Hausdorff distances

with Henry Adams, Sushovan Majhi, and Nicholas McBride

Discrete Comput. Geom. (2025), to appear.

arXiv 2309.16648

Colorful Borsuk–Ulam theorems and applications

with Zoe Wellner

J. Fixed Point Theory Appl. 27, 81 (2025).

arXiv 2309.14539

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, and Ling Zhou

Algebr. Geom. Topol., to appear.

arXiv 2301.00246

Transversal generalizations of hyperplane equipartitions

with Samuel Murray, Steven Simon, and Laura Stemmler

Int. Math. Res. Not. IMRN 2024(7), 5586–5618 (2024).

arXiv 2210.15423

Unit sphere fibrations in Euclidean space

with Daniel Asimov, Michael Harrison, and Wesley Pegden

Proc. Edinb. Math. Soc. 67, 287–298 (2024).

arXiv 2210.13981

Random complexes with free involution

with Andrew Newman

Israel J. Math. (2023), to appear.

arXiv 2210.11316

Vietoris thickenings and complexes have isomorphic homotopy groups

with Henry Adams and Žiga Virk

J. Appl. Comput. Topol. 7, 221–241 (2023).

arXiv 2206.08812

Colorful words and d-Tverberg complexes

with Amzi Jeffs

Comb. Theory 4(1), Paper No. 3, 13 p. (2024).

arXiv 2205.04776

Vertex numbers of simplicial complexes with free abelian fundamental group

with Matt Superdock

Ars. Math. Contemp. 25, #1.05, 16 p. (2025).

arXiv 2109.11952

On inscribed trapezoids and affinely 3-regular maps

with Michael Harrison

Proc. Roy. Soc. Edinburgh Sect. A 154, 1024–1032 (2024).

arXiv 2109.05985

Embedding dimensions of simplicial complexes on few vertices

with Mirabel Hu, Verity Scheel, and Steven Simon

Ann. Comb. 27, 993–1003 (2023).

arXiv 2109.04855

Coupled embeddability

with Michael Harrison

Bull. Lond. Math. Soc. 54 (5), 1609–1629 (2022).

arXiv 2107.09816

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

with Henry Adams and Johnathan Bush

Michigan Math. J. 74(4), 775–796 (2024).

arXiv 2106.14677

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

with Michael Harrison

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

arXiv 2010.11996

What can you draw?

with Fei Peng

Amer. Math. Monthly 130 (1), 5–19 (2023).

arXiv 2004.01049

The geometry of fair division

Snapshots of modern mathematics from Oberwolfach 2023 (7).

DOI 10.14760/SNAP-2023-007-EN

Metric thickenings, Borsuk–Ulam theorems, and orbitopes

with Henry Adams and Johnathan Bush

Mathematika 66, 79–102 (2020).

arXiv 1907.06276

A nonlinear Lazarev–Lieb theorem: L²-orthogonality via motion planning

with Matt Superdock

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

arXiv 1906.04417

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).

arXiv 1902.00935

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 1809.03268

Barycenters of points in polytope skeleta

with Michael Gene Dobbins

Contemp. Math. 764, 83–88 (2021).

arXiv 1809.01613

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).

arXiv 1806.02484

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 1803.11516

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 1712.03456

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

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

arXiv 1710.09434

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

with Shira Zerbib

Combinatorica 39 (3), 627–637 (2019).

arXiv 1710.07722

Metric reconstruction via optimal transport

with Michał Adamaszek and Henry Adams

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

arXiv 1706.04876

Achieving rental harmony with a secretive roommate

with Kelsey Houston-Edwards and Frédéric Meunier

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

arXiv 1702.07325

On affine Tverberg-type results without continuous generalization

Manuscript; to be rewritten.

arXiv 1702.05466

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

with M. Asada, V. Pisharody, M. Polevy, D. Stoner, L. H. Tsang, and Z. Wellner

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

arXiv 1701.04955

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

with M. Asada, R. Chen, F. Huang, M. Polevy, D. Stoner, L. H. Tsang, and Z. Wellner

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

arXiv 1608.04279

Minkowski complexes and convex threshold dimension

with Raman Sanyal

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

arXiv 1607.07814

Intersection patterns of finite sets and of convex sets

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

arXiv 1607.01003

On homotopy types of Euclidean Rips complexes

with Michał Adamaszek and Adrien Vakili

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

arXiv 1602.04131

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 1510.07984

Hyperplane mass partitions via relative equivariant obstruction theory

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

Documenta Math. 21, 735–771 (2016).

arXiv 1509.02959

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 1502.02975

Counterexamples to the topological Tverberg conjecture

Oberwolfach Reports 12 (1), 318–321 (2015).

arXiv 1502.00947

Nerve complexes of circular arcs

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

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

arXiv 1410.4336

Tverberg plus constraints

with Pavle Blagojević and Günter M. Ziegler

Bull. Lond. Math. Soc. 46 (5), 953–967 (2014).

arXiv 1401.0690

A minimal irreducible triangulation of S³

Combinatorial Methods in Topology and Algebra, Springer INdAM Series 12, 49–52 (2015).