I moved to Carnegie Mellon University. This is my new website.

I am an Assistant Professor in the Department of Mathematical Sciences at Carnegie Mellon University. Before that I was an H.C. Wang Assistant Professor at Cornell University and a Ph.D. student at TU Berlin.

During the Fall semester 2017 I was at MSRI in Berkeley.

My Google Scholar profile

My CV

## Summer Program for Undergraduate Research

I will again lead a project on Topological Methods in Discrete Geometry in Cornell's Summer Program for Undergraduate Research from June 4 – July 27, 2018.

For results of the 2016 and 2017 editions of SPUR's Topological Methods in Discrete Geometry project, see here.

## About my Work

I Bárány, PVM Blagojević, GM Ziegler,
Tverberg's Theorem at 50: Extensions and Counterexamples.
*Notices Amer. Math. Soc.* 63.7 (2016): 732−739.

Survey about counterexamples to the topological Tverberg conjecture and extensions of Tverberg's Theorem using the constraint method.

Gil Kalai's blog, From Oberwolfach: The Topological Tverberg Conjecture is False.

PVM Blagojević, GM Ziegler,
Beyond the Borsuk-Ulam theorem: The topological Tverberg story.
to appear in *Journey Through Discrete Mathematics. A Tribute to Jiří Matoušek* (Martin Loebl, Jaroslav Nešetřil, Robin Thomas, eds.), Springer 2017.

R. Živaljević,
Topological methods in discrete geometry.
*Handbook of Discrete and Computational Geometry* (edited by Jacob E. Goodman, Joseph O'Rourke, and Csaba D. Tóth)

Expository survey including the constraint method (or Gromov−Blagojević−Frick−Ziegler reduction),
counterexamples to the topological Tverberg conjecture, and the AP conjecture,
which I recently resolved.

Splitting Rent with Triangles.
Episode of *PBS Infinite Series* about fairly dividing rent, which also presents my
research with undergraduates during the Summer of 2016 on fair rent divisions.
See also this supplemental note coauthored with Kelsey Houston-Edwards.

## Teaching

Fall 2018:

21-752 − Algebraic Topology

## Publications & Preprints

### Preprints

Splitting loops and necklaces: Variants of the square peg problem

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

Preprint, 11 pages, submitted

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

with Aaron Chen and Anne Shiu

Preprint, 20 pages, submitted

On affine Tverberg-type results without continuous generalization

Preprint, 13 pages, submitted

### Journal Publications

Metric reconstruction via optimal transport

with Michal Adamaszek and Henry Adams

*SIAM J. Appl. Alg. Geom.*, accepted pending minor revisions, 20 pages

On the generalized Erdős−Kneser conjecture: proofs and reductions

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

*J. Combin. Theory, Ser. B*, accepted pending minor revisions, 8 pages

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

*Int. Math. Res. Not. IMRN*, online first, 25 pages

arXiv version

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

with Shira Zerbib

*Combinatorica*, to appear, 9 pages

Achieving rental harmony with a secretive roommate

with Kelsey Houston-Edwards and Frédéric Meunier

*Amer. Math. Monthly*, to appear, 15 pages

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)*, to appear, 6 pages

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

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"

## Videos of Talks

Intersections of Finite Sets: Geometry and Topology

Geometric And Topological Combinatorics: Modern Techniques And Methods, MSRI, October 9, 2017

Metric reconstruction via optimal transport

Topology and Geometry in a Discrete Setting, ICERM, December 1, 2016

Intersection patterns of finite sets and of convex sets

Transversal, Helly and Tverberg type Theorems in Geometry, Combinatorics and Topology III, CMO Oaxaca, Mexico, October 25, 2016

Topology and combinatorics of fair division

Applied Algebraic Topology Research Network, online seminar

Counterexamples to the topological Tverberg conjecture

JMM Seattle, AMS Special Session on Algebraic and Topological Methods in Combinatorics, January 8, 2016

## Posters

Triangulations with valence bounds

Presented at Discrete, Computational and Algebraic Topology (Copenhagen, November 2014)

A minimal irreducible triangulation of S^{3}

Presented at CoMeTA 2013 and the ERC Workshop Delaunay Geometry − Polytopes, Triangulations, and Spheres