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

• 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.