Prof. Dr. Christian Haase DFG-Heisenberg-Professur für Diskrete Methoden in Algebra und algebraischer Geometrie FB 12 - Institut für Mathematik Goethe-Universität Robert-Mayer-Str. 10 D-60325 Frankfurt am Main Fon: +49 (069) 798-23411 Fon: +49 (069) 798-22526 (Sekr.) Fax: +49 (069) 798-28841 Büro: R-M 10, Raum 405 Sprechstunde: Di 16-17 und n.V.

Contents

• Upcoming
  • arXiv-Club diskrete Mathematik
  • Schüler-AG "Fastfood, quadratische Magie und Gitterpunkte" 3.-5.4.2012, Frankfurt
  • Algebraic Geometry & Combinatorics, March 17-24, 2013, Haus Bergkranz
  • MEGA 2013: Effective Methods in Algebraic Geometry, June 3-7, 2013, Goethe University Frankfurt
• Research
  • Interests
  • Publications & Preprints
  • Activities
• Teaching
  • Current Teaching
  • Former Teaching
  • Bachelor/Master Thesis Projects
  • Students & Postdocs mentored

Research

Research Interests

• Lattice Polytopes
• Toric Algebra
• Tropical Geometry
• Combinatorial Commutative Algebra
• Algorithmic Algebra
• Geometric and Topological Combinatorics

Reports & Preprints

• 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.
• Polyhedral adjunction theory [arXiv]
  Sandra Di Rocco, Christian Haase, Benjamin Nill, and Andreas Paffenholz
  24 pages, 8 figures.
• Few smooth d-polytopes with N lattice points [arXiv]
  Tristram Bogart, Christian Haase, Milena Hering, Benjamin Lorenz, Benjamin Nill, Andreas Paffenholz, Francisco Santos, and Hal Schenck
  19 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.

Publications

• Linear Systems on Tropical Curves [arXiv]
  Christian Haase, Gregg Musiker, and Josephine Yu
  Mathematische Zeitschrift Online First DOI 10.1007/s00209-011-0844-4
• 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.
• 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.
• On Fanos and Chimneys [pdf]
  Christian Haase and Andreas Paffenholz
  Oberwolfach Reports, in Report 39/2007 edited by Ben Howard: 2303-2306.
• Gröbner Basis for 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.
• Lattices generated by skeletons of reflexive polytopes [arXiv]
  Christian Haase and Benjamin Nill
  Journal of Combinatorial Theory, Series A , 115:340-344, 2008.
• 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.
• The reflexive dimension of a lattice polytope [arXiv pdf]
  Christian Haase and Ilarion Melnikov
  Annals of Combinatorics, 10:211-217, 2006.
• 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.
• On the maximal width of empty lattice simplices [pdf]
  Christian Haase and Günter Ziegler
  European J. Combinatorics, 21(1):111-119, 2000.
• 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.

Activities

under construction

Teaching

Current Teaching

• VL Local Cohomology of Semigroup Rings [OLAT]
• SE Toric Ideals [OLAT]

Former Teaching

under construction (siehe Forschung & Lehre)

Bachelor/Master Thesis Projects

under construction

Students & Postdocs mentored

• Postdocs
  • Felix Breuer (2009-2010)
  • Andreas Paffenholz (2005-2010)
  • Benjamin Nill (2005-2009)
• Students
  • Benjamin Lorenz (MSc, PhD 2008-)
  • Kaie Kubjas (PhD 2009-, with Klaus Altmann)
  • Matthias Lenz (MSc 2006-2007)
  • Lindsay Piechnik (BSc 2003-2004)

 

geändert am 21. Februar 2012  E-Mail: Sekretariatweber@mi.informatik.uni-frankfurt.de

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