I am an H.C. Wang Assistant Professor (non-tenure-track) at the Department of Mathematics at Cornell University. Before that I was a Ph.D. student at TU Berlin.

During the Fall semester 2017 I am 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 19 – August 11, 2017.

For results of the 2016 edition 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

Spring 2017:
MATH 7620 - Selected Topics in Discrete and Metric Geometry
I co-organize the Putnam Practice Sessions

Publications & Preprints

Preprints

Metric reconstruction via optimal transport
with Michal Adamaszek and Henry Adams
Preprint, 20 pages

Achieving rental harmony with a secretive roommate
with Kelsey Houston-Edwards and Frédéric Meunier
Preprint, 11 pages

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

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
Preprint, 18 pages

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
Preprint, 10 pages

Topology of the Grünbaum−Hadwiger−Ramos hyperplane mass partition problem
with Pavle Blagojević, Albert Haase, and Günter M. Ziegler
Preprint, 27 pages

Journal Publications

On homotopy types of Euclidean Rips complexes
with Michal Adamaszek and Adrien Vakili
Discrete Comput. Geom., to appear, 14 pages
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), to appear, 6 pages

Minkowski complexes and convex threshold dimension
with Raman Sanyal
J. Combin. Theory, Ser. A 151 (2017), 202−206
arXiv version

Intersection patterns of finite sets and of convex sets
Proc. Amer. Math. Soc. 145(7) (2017), 2827−2842
arXiv version

Hyperplane mass partitions via relative equivariant obstruction theory
with Pavle Blagojević, Albert Haase, and Günter M. Ziegler
Documenta Math. 21 (2016), 735−771
arXiv version

Nerve complexes of circular arcs
with Michal Adamaszek, Henry Adams, Chris Peterson, and Corrine Previte-Johnson
Discrete Comput. Geom. 56(2) (2016), 251−273
arXiv version

Tverberg plus constraints
with Pavle Blagojević and Günter M. Ziegler
Bull. London Math. Soc. 46 (2014), 953−967
arXiv version

Conference Proceedings

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

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

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 S3
Presented at CoMeTA 2013 and the ERC Workshop Delaunay Geometry − Polytopes, Triangulations, and Spheres