preprints
- From linear programming to colliding particles
(with
Alex Black
and Niklas Lütjeharms)
[arXiv]
- Inscribable fans II: Inscribed zonotopes, simplicial arrangements, and reflection groups
(with
Sebastian Manecke)
[arXiv]
- Generalized angle vectors, geometric lattices, and
flag-angles
(with
Spencer Backman and
Sebastian Manecke)
[arXiv]
- Whitney numbers of arrangements via measure concentration
of intrinsic volumes
(with Karim
Adiprasito)
[arXiv]
published
- Spectral Polyhedra
(with James Saunderson)
Forum of Mathematics, Sigma, accepted for publication.
[arXiv]
- Underlying Flag Polymatroids
(with
Alex Black)
Advances in Mathematics 2024, online first.
[journal]
[arXiv]
- Inscribable fans I: Inscribed cones, virtual polytopes, and routed
particle trajectories
(with
Sebastian Manecke)
Mathematika (2024).
[journal]
[arXiv]
- Fan Valuations and spherical intrinsic volumes
(with
Spencer Backman and
Sebastian Manecke)
Annals of Combinatorics (2024).
[journal]
[arXiv]
- Kalai's 3^d-conjecture for unconditional and locally anti-blocking polytopes
(with
Martin Winter)
Proceedings of the AMS, accepted for publication.
[arXiv]
- The Polyhedral Geometry of Pivot Rules and Monotone Paths
(with
Alex Black,
Jesús A. De Loera, and Niklas Lütjeharms)
SIAM J. on Applied Algebra and Geometry (SIAGA),
Volume 7, Issue 3, Sept 2023.
[journal]
[arXiv]
- Linear Principal Minor Polynomials: Hyperbolic Determinantal Inequalities and Spectral Containment
(with
Greg Blekherman,
Mario Kummer, Kevin Shu, and
Shengding Sun)
International Mathematics Research Notices 2022, online first.
[journal]
[arXiv]
- Tropical Carathéodory with Matroids
(with Georg Loho)
Discrete & Computational Geometry 2022, online first.
[journal]
[arXiv]
- Geometric Inequalities for Anti-Blocking Bodies
(with
Shiri Artstein-Avidan and
Shay Sadovsky)
Communications in Contemporary Mathematics 2022, online ready.
[journal]
[arXiv]
- Standard complexes of matroids and lattice paths
(with Alex Engström and
Christian Stump)
Vietnam J. Math 50, 763-779, 2022 (Sturmfels 60th birthday issue).
[journal]
[arXiv]
- Coprime Ehrhart theory and counting free segments
(with
Sebastian Manecke)
International Mathematics Research Notices (2022), online first.
[journal]
[arXiv]
- S-hypersimplices, pulling triangulations, and monotone paths
(with
Sebastian Manecke and Jeonghoon So)
Electron. J. Combin.,
Volume 27, Issue 3 (2020), Paper #P3.16
[journal]
[arXiv]
- On piecewise-linear homeomorphisms between distributive and anti-blocking polyhedra
(with
Christoph Pegel)
Combinatorial Structures in Algebra and Geometry. NSA 2018.
Stamate D., Szemberg T. (eds).
Springer
Proceedings in Mathematics & Statistics, vol 331. pp. 95-114
[journal]
[arXiv]
- Unconditional reflexive polytopes
(with
Florian Kohl and
McCabe Olsen)
Branko Grünbaum Memorial Issue,
Discrete & Computational Geometry, Vol 64, 2020, pp. 427-452
[journal]
[arXiv]
- The Martin Gardner Polytopes
(with Kristin Fritsch, Janin Heuer, and Nicole Schulz)
The American Mathematical Monthly, Vol 127, Issue 7, 2020, pp. 594-601
[journal]
[arXiv]
- On f- and h-vectors of relative simplicial complexes
(with
Giulia Codenotti,
Lukas Katthän)
Algebraic Combinatorics, Volume 2 (2019) no. 3, pp. 343-353
[journal]
[arXiv]
- Lipschitz polytopes of posets and permutation
statistics
(with Christian Stump)
Journal of Combinatorial Theory, Series A 158 (2018) 605-620
[journal]
[arXiv]
- Combinatorial mixed valuations
(with Katharina
Jochemko)
Advances in Mathematics, 319 (2017), pp. 630-652
[journal]
[arXiv]
-
Colorful simplicial depth, Minkowski sums, and generalized
Gale transforms
(with
Karim Adiprasito,
Philip Brinkmann,
Arnau Padrol,
Pavel Paták,
Zuzana Patáková)
International Mathematics Research Notices, 6 (2019), pp. 1894-1919
[journal]
[arXiv]
- Extension complexity and realization spaces of
hypersimplices
(with
Francesco Grande and
Arnau Padrol)
Discrete & Computational Geometry, Vol 59, No 3, 2018, pp. 621-642
[journal]
[arXiv]
- Reflection groups, arrangements, and invariant real
varieties
(with
Tobias Friedl and
Cordian Riener)
Proceedings of the AMS, Vol 146, 2018, pp. 1031-1045
[journal]
[arXiv]
- Two double poset polytopes
(with Tom Chappell
and
Tobias Friedl
)
SIAM J. Discrete Math. 31-4 (2017), pp. 2378-2413
[journal]
[arXiv]
- On degree sequences of undirected, directed, and
bidirected graphs (with
Laura Gellert)
European Journal of Combinatorics 64 (2017) 113-124
[journal]
[arXiv]
- Minkowski complexes and convex threshold dimension
(with Florian Frick)
Journal of Combinatorial Theory, Series A 151 (2017) 202-206
[journal]
[arXiv]
- Mixed
Ehrhart polynomials
(with Christian
Haase, Martina
Juhnke-Kubitzke, and
Thorsten Theobald)
Electron. J. Combin.,
Volume 24, Issue 1 (2017), Paper #P1.10
[journal]
[arXiv]
- Theta
rank, levelness, and matroid minors
(with
Francesco Grande)
J. Combin. Theory Ser. B 123 (2017), 1-31.
[journal]
[arXiv]
- Relative
Stanley-Reisner theory and Upper Bound Theorems for
Minkowski sums
(with Karim
Adiprasito)
Publ. Math. Inst. Hautes Etudes Sci. (2016) 124: 99-163.
[journal]
[arXiv]
-
Combinatorial
positivity of translation-invariant valuations and a
discrete Hadwiger theorem
(with Katharina
Jochemko)
J. Eur. Math. Soc. (JEMS), June 2018 (online first).
[arXiv]
[journal]
- Deciding
polyhedrality of spectrahedra
(with Avinash
Bhardwaj and Philipp
Rostalski)
SIAM J. Opt. 25 (2015), no. 3, 1873-1884.
[journal]
[journal-version]
[arXiv]
- Arithmetic of
marked order polytopes, monotone triangle reciprocity, and
partial colorings
(with
Katharina Jochemko)
SIAM J. Discrete Math. 28 (2014), no. 3, 1540-1558,
[journal]
[arXiv]
- Laplacian ideals,
arrangements, and resolutions
(with Anton
Dochtermann)
J. Algebraic Combin. 40 (2014), no. 3, 805-822. [journal]
[arXiv]
- Smooth
Hyperbolicity Cones are Spectrahedral
Shadows
(with Tim
Netzer)
Special issue `Lifts of Convex Sets in Optimization'
Math. Prog. B 153 (2015), Issue 1, 213-221.
[journal]
[arXiv]
- An
Alexander-type duality for valuations
(with Karim
Adiprasito)
Proceedings of the AMS, Vol 143, No 2, 2015, pp.
833-843.
[journal]
[arXiv]
- The
Entropic Discriminant
(with Bernd
Sturmfels and Cynthia
Vinzant)
Advances in Mathematics, 244 (2013), pp. 678-707.
[journal]
[arXiv]
- Tropical types and
associated cellular resolutions
(with A.
Dochtermann and Michael
Joswig)
Journal of Algebra, 356 (2012), pp. 304-324.
[journal]
[arXiv]
- On the
derivative cones of polyhedral cones
Advances in Geometry, Vol 13 (2013), pp. 315-321. [journal]
[arXiv]
- Non-projectability
of polytope skeleta
(with Thilo
Rörig)
Advances in Mathematics, 229 (2012), pp. 79-101.
[journal]
[arXiv]
- Orbitopes
(with Bernd
Sturmfels and Frank
Sottile)
Mathematika, Vol 57, No 2, 2011, pp. 257-314. [journal]
[arXiv]
- Ehrhart theory,
modular flow reciprocity, and the Tutte
polynomial
(with Felix
Breuer)
Mathematische Zeitschrift, 270 (2012), pp. 1-18. [journal]
[arXiv]
- Construction and
Analysis of Projected Deformed Products
(with Günter M.
Ziegler)
Discrete & Computational Geometry, Vol 43, No 2, 2010,
pp. 412-435, [journal]
[arXiv]
- On
Kalai's conjectures concerning centrally symmetric
polytopes
(with Axel
Werner and Günter M.
Ziegler)
Discrete & Computational Geometry, Vol 41, No 2, 2009,
pp. 183-198. [journal]
[arXiv]
- Combinatorial
Stokes formulas via minimal resolutions
(with Bernhard
Hanke, Carsten
Schultz, and Günter M.
Ziegler)
Journal of Combinatorial Theory, Series A 116 (2009), pp.
404-420. [journal]
[arXiv]
- Topological
obstructions for vertex numbers of Minkowski
sums
Journal of Combinatorial Theory, Series A 116 (2009), pp.
168-179. [journal]
[arXiv]
misc
- On the Combinatorics of Projected Deformed
Products
Diploma Thesis, August 2005, 57 pages, PDF
- Constructions and obstructions for extremal
polytopes
PhD Thesis, May 2008, 79+6 pages, Published
online,
PDF