# preprints

**Flag Polymatroids**(with Alex Black) [arXiv]**Inscribable Fans II: Inscribed zonotopes, simplicial arrangements, and reflection groups**(with Sebastian Manecke) [arXiv]**The Polyhedral Geometry of Pivot Rules and Monotone Paths**(with Alex Black, Jesús A. De Loera, and Niklas Lütjeharms) [arXiv]**Linear Principal Minor Polynomials: Hyperbolic Determinantal Inequalities and Spectral Containment**(with Greg Blekherman, Mario Kummer, Kevin Shu, and Shengding Sun) [arXiv]**Fan Valuations and spherical intrinsic volumes**(with Spencer Backman and Sebastian Manecke) [arXiv]**Inscribable fans I: Inscribed cones, virtual polytopes, and routed particle trajectories**(with Sebastian Manecke) [arXiv]**Spectral Polyhedra**(with James Saunderson) [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

**Tropical Carathéodory with Matroids**(with Georg Loho)

Discrete & Computational Geometry, accepted for publication. [arXiv]**Geometric Inequalities for Anti-Blocking Bodies**(with Shiri Artstein-Avidan and Shay Sadovsky)

Communications in Contemporary Mathematics, accepted for publication. [arXiv]**Standard complexes of matroids and lattice paths**(with Alex Engström and Christian Stump)

Vietnam J. Math (Sturmfels 60th birthday), 2022, online first. [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