Research Interests

• Discrete and Convex Methods in Algebraic Geometry
• Combinatorial Commutative Algebra
• Toric Algebra
• Tropical Geometry
• Lattice Polytopes
• Algebraic Statistics
• Algorithmic Algebra
• Geometric and Topological Combinatorics

Reviewed Publications

• Lower Bounds on the Depth of Integral ReLU Neural Networks via Lattice Polytopes. C. Haase, C. Hertrich, G. Loho (2023). The Eleventh International Conference on Learning Representations, ICLR 2023, Kigali, Rwanda, May 1-5, 2023. OpenReview.net 2023. https://openreview.net/forum?id=2mvALOAWaxY

• Fine Polyhedral Adjunction Theory. S. Garzón Mora, C. Haase (2023). Proceedings of the 35th Conference on Formal Power Series and Algebraic Combinatorics (Davis). Séminaire Lotharingien de Combinatoire 89B, Article #62, 12 pp., https://www.mat.univie.ac.at/~slc/wpapers/FPSAC2023/62.pdf

• Competitive equilibrium always exists for combinatorial auctions with graphical pricing schemes. M.-C. Brandenburg, C. Haase, N, Mai Tran (2022). La Matematica. Springer. https://doi.org/10.1007/s44007-022-00038-7
• Existence of unimodular triangulations - positive results. C. Haase, A. Pfaffenholz, L.C. Piechnik, F. Santos. Memoirs of the American Mathematical Society, Vol. 270, Number 1321, 1261–1280 (2021). https://www.ams.org/books/memo/1321/
• Algebraic Hyperbolicity for Surfaces in Toric Threefolds. C. Haase, N. Ilten. J. Algebraic Geom. 30 (2021), 573-602. https://doi.org/10.1090/jag/770
• The Finiteness Threshold Width of Lattice Polytopes. Mónica Blanco, Christian Haase, Jan Hofmann, Francisco Santos. Accepted by AMS (2020) https://arxiv.org/abs/1607.00798
• Levelness of Order Polytopes .C. Haase, F. Kohl, A. Tsuchiya (2020), Siam Journal on Discrete Mathematics, Vol. 34, Issue 2, 1261–1280. https://doi.org/10.1137/19M1292345
• Maximum Number of Modes of Gaussian Mixtures. C. Amendola, A. Engström and C. Haase. Information and Inference: A Journal of the IMA, iaz013 (2019), https://doi.org/10.1093/imaiai/iaz013
• M. Beck, C. Haase, A. Higashitani, J. Hofscheier, K. Jochemko, L. Katthän, M. Michałek (2019): Smooth centrally symmetric polytopes in dimension 3 are IDP.Annals of Combinatorics, No 26, pp 1-8. https://doi.org/10.1007/s00026-019-00418-x
• Discrete Mixed Volume and Hodge-Deligne Numbers. Sandra Di Rocco, Christian Haase, Benjamin Nill. Advances in Applied Mathematics, Vol. 104, Pages 1-13. (2019) https://doi.org/10.1016/j.aam.2018.11.002
• J. Erbe, C. Haase, F. Santos (2019): Ehrhart-equivalent 3-polytopes are equidecomposable. Proc. Amer. Math. Soc. 147 (2019), 5373-5383. https://doi.org/10.1090/proc/14626
• Mixed Ehrhart polynomials. C. Haase, M. Juhnke-Kubitzke, R. Sanyal, T. Theobald. The Electronic Journal of Combinatorics Volume 24, Issue 1 (2017) Paper #P1.10
• Convex-normal (pairs of) polytopes, Christian Haase, Jan Hofmann.  Canadian Mathematical Bulletin. Vol. 60, Issue 3, pp. 510-521 (2017). http://dx.doi.org/10.4153/CMB-2016-057-0
• Finitely many smooth d-polytopes with n lattice points, Tristram Bogart, Christian Haase, Milena Hering, Benjamin Lorenz, Benjamin Nill, Andreas Paffenholz, Günter Rote, Francisco Santos, Hal Schenck Israel Journal of Mathematics Vol. 207, Issue 1, pages 301-329, (2015).
• Polyhedral adjunction theory, Sandra Di Rocco, Christian Haase, Benjamin Nill and Andreas Paffenholz Algebra & Number Theory Vol. 7, No. 10, pages 2417–2446, (2014)
• Polytopes associated to dihedral groups, Barbara Baumeister, Christian Haase, Benjamin Nill, Andreas Paffenholz. Ars Mathematica Contemporanea 7, No 1, pages 30–38, (2014).
• Integer Decomposition Property of Dilated Polytopes, David A. Cox,Christian Haase, Takayuki Hibi, Akihiro Higashitani. Electronic Journal of Combinatorics Vol. 21, Issue 4, Paper #P4.28, (2014).
• Linear Systems on Tropical Curves [arXiv]
  Christian Haase, Gregg Musiker, and Josephine Yu
  Mathematische Zeitschrift Volume 270, Issue 3-4, pp 1111-1140, 2012.
• Lattice Polygons and the number 2i+7 [arXiv talk]
  Christian Haase and Josef Schicho
  American Mathematical Monthly February: 151 - 165, 2009.
• 
  (Theorems of Brion, Lawrence, and Varchenko on rational generating functions for cones) [arXiv]
  Matthias Beck, Christian Haase, and Frank Sottile
  The Mathematical Intelligencer, 31:9-17, 2009.
• Cayley decompositions of lattice polytopes and upper bounds for h*-polynomials [arXiv]
  Christian Haase, Benjamin Nill, and Sam Payne
  Journal für die reine und angewandte Mathematik, 637:207-216, 2009.
• Grid graphs, Gorenstein polytopes, and domino stackings [arXiv]
  Matthias Beck, Christian Haase, and Steven V. Sam
  Graphs and Combinatorics, 25(4):409-426, 2009.
• Quadratic Gröbner bases for smooth 3×3 transportation polytopes [arXiv]
  Christian Haase and Andreas Paffenholz
  Journal of Algebraic Combinatorics , 30(4):477-489, 2009.
• On permutation polytopes [arXiv pdf data]
  Barbara Baumeister, Christian Haase, Benjamin Nill, and Andreas Paffenholz
  Advances in Mathematics , 222:431-452, 2009.
• Lattice Points in Minkowski Sums [arXiv]
  Christian Haase, Benjamin Nill, Andreas Paffenholz, and Francisco Santos
  Electronic Journal of Combinatorics, 15:#N11, 2008.
• Dedekind-Carlitz Polynomials as Lattice-Point Enumerators in Rational Polyhedra [arXiv]
  Matthias Beck, Christian Haase, and Asia R. Matthews
  Mathematische Annalen, 341:945-961, 2008.
• Quasi-period collapse and GL(n,Z)-scissors congruence in rational polytopes [arXiv]
  Christian Haase and Tyrrell McAllister
  Contemporary Mathematics, 452:115-122, 2008.
• Lattices generated by skeletons of reflexive polytopes [arXiv]
  Christian Haase and Benjamin Nill
  Journal of Combinatorial Theory, Series A , 115:340-344, 2008.
• On Fanos and Chimneys [pdf]
  Christian Haase and Andreas Paffenholz
  Oberwolfach Reports, in Report 39/2007 edited by Ben Howard: 2303-2306.
• The reflexive dimension of a lattice polytope [arXiv pdf]
  Christian Haase and Ilarion Melnikov
  Annals of Combinatorics, 10:211-217, 2006.
• Integral affine structures on spheres: complete intersections [arXiv]
  Christian Haase and Ilia Zharkov
  DUKE-CGTP-05-03
  IMRN, 2005(51):3153-3167, 2005.
• Problems from the Cottonwood Room [pdf]
  Matthias Beck, Beifang Chen, Lenny Fukshansky, Christian Haase, Allen Knutson, Bruce Reznick, Sinai Robins, and Achill Schürmann
  Contemporary Mathematics, 374:179-191, 2005.
• Polar decomposition and Brion's theorem [arXiv]
  Christian Haase
  Contemporary Mathematics , 374:91-99, 2005.
• Examples and Counterexamples for the Perles Conjecture [arXiv data]
  Christian Haase and Günter Ziegler
  Discrete and Computational Geometry, 28(1):29-44, 2002.
• All toric l.c.i.-singularities admit projective crepant resolutions [arXiv]
  Dimitrios Dais, Christian Haase, and Günter Ziegler
  Tohôku Math. J., 53(1):95-107, 2001.
• On the maximal width of empty lattice simplices [pdf]
  Christian Haase and Günter Ziegler
  European J. Combinatorics, 21(1):111-119, 2000.

Nonreviewed Publication

• Research Report 2005-2008 [pdf]
  Christian Haase and the Research Group Lattice Polytopes
  16 pages, December 2008.
• Permutation Polytopes of Cyclic Groups [arXiv]
  Barbara Baumeister, Christian Haase, Benjamin Nill, and Andreas Paffenholz
  15 pages.
• Integral affine structures on spheres and torus fibrations of Calabi-Yau toric hypersurfaces II [arXiv]
  Christian Haase and Ilia Zharkov
  DUKE-CGTP-03-01, 21 pages.
• Integral affine structures on spheres and torus fibrations of Calabi-Yau toric hypersurfaces I [arXiv]
  Christian Haase and Ilia Zharkov
  DUKE-CGTP-02-05, 26 pages.