Publikationen
2020
Begutachteter Zeitschriftenartikel
Gorenstein polytopes with trinomial h -polynomials
In: Beiträge zur Algebra und Geometrie - Berlin: Springer . - 2020
On defectivity of families of full-dimensional point configurations
In: Proceedings of the American Mathematical Society / B/ American Mathematical Society - Providence, RI: Soc., Bd. 7.2020, S. 43-51
The mixed degree of families of lattice polytopes
In: Annals of combinatorics: AC - [Cham (ZG)]: [Springer International Publishing AG], Bd. 24.2020, S. 203-216
Dissertation
Mixed lattice polytope theory with a view towards sparse polynomial systems
In: Magdeburg, 2020, XV, 136 Seiten, Diagramme, 30 cm ; [Literaturverzeichnis: Seite 109-113]
2019
Begutachteter Zeitschriftenartikel
A note on discrete mixed volume and Hodge-Deligne numbers
In: Advances in applied mathematics - Amsterdam [u.a.]: Elsevier, 1980, Bd. 104.2019, S. 1-13
Nicht begutachteter Zeitschriftenartikel
Generalized flatness constants, spanning lattice polytopes, and the Gromov width
In: De.arxiv.org - [S.l.]: Arxiv.org, 1991, 2019, article 1911.03511, 11 Seiten
2018
Begutachteter Zeitschriftenartikel
Lattice simplices with a fixed positive number of interior lattice points - a nearly optimal volume bound
In: International mathematics research notices: IMRN - Oxford: Oxford University Press, 1991 . - 2018
On Ehrhart polynomials of lattice triangles
In: The electronic journal of combinatorics - [Madralin]: EMIS ELibEMS, 1994, Vol. 25.2018, 1, Art. P1.3, insgesamt 8 S.
Smooth polytopes with negative Ehrhart coefficients
In: Journal of combinatorial theory / A - Amsterdam [u.a.]: Elsevier, 1971, Bd. 160.2018, S. 316-331
Habilitation
Modern aspects of classical convex geometry
In: Magdeburg, 2017, xxxii, 153 Seiten, Illustrationen, 30 cm ; [Literaturverzeichnis: Seite 131-136]
2017
Begutachteter Zeitschriftenartikel
Ehrhart theory of spanning lattice polytopes
In: International mathematics research notices: IMRN - Oxford: Oxford University Press, 2017
Minimality and mutation-equivalence of polygons
In: Forum of mathematics / Sigma - Cambridge: Cambridge Univ. Press, 2013, Vol. 5.2017, Art. e18, insgesamt 48 S.
2015
Begutachteter Zeitschriftenartikel
A bound for the splitting of smooth Fano polytopes with many vertices
In: Journal of algebraic combinatorics - Dordrecht [u.a.]: Springer Science + Business Media B.V, 1992 . - 2015, insges. 20 S.
Finitely many smooth d-polytopes with n lattice points
In: Israel journal of mathematics - Berlin: Springer, 1963, Bd. 207.2015, 1, S. 301-329
Largest integral simplices with one interior integral point - solution of Hensley's conjecture and related results
In: Advances in mathematics - Amsterdam [u.a.]: Elsevier, 1961, Bd. 274.2015, S. 118-166, 2014
On smooth {G}orenstein polytopes
In: Tohoku Math. J. (2), Vol. 67, 2015, Issue 4, S. 513--530, ISSN 0040-8735, 10.2748/tmj/1450798070
The degree of point configurations - Ehrhart theory, Tverberg points and almost neighborly polytopes
In: European journal of combinatorics - London: Academic Press, Bd. 50.2015, S. 159-179
2014
Begutachteter Zeitschriftenartikel
On the equality case in Ehrhart's volume conjecture
In: Advances in Geometry, Vol. 14, 2014, Issue 4, S. 579-586, 10.1515/advgeom-2014-0001
Polytopes associated to dihedral groups
In: Ars Mathematica Contemporanea, Vol. 7, 2014, Issue 1, S. 30-38
2013
Begutachteter Zeitschriftenartikel
Gorenstein polytopes and their stringy E-functions
In: Mathematische Annalen, Vol. 355, 2013, Issue 2, S. 457-480, 10.1007/s00208-012-0792-2
Polyhedral adjunction theory
In: Algebra and Number Theory, Vol. 7, 2013, Issue 10, S. 2417-2446, 10.2140/ant.2013.7.2417
Buchbeitrag
Fano polytopes
In: 2013, S. 349--364
2012
Begutachteter Zeitschriftenartikel
A relation between number of integral points, volumes of faces and degree of the discriminant of smooth lattice polytopes
In: Comptes Rendus Mathematique, Vol. 350, 2012, Issue 5-6, S. 229-233, 10.1016/j.crma.2012.02.001
Lattice-width directions and minkowski's 3 d-theorem
In: SIAM Journal on Discrete Mathematics, Vol. 26, 2012, Issue 3, S. 1104-1107, 10.1137/120877635
Reflexive polytopes of higher index and the number 12
In: Electronic Journal of Combinatorics, Vol. 19, 2012, Issue 3, S. 1-18
Buchbeitrag
Permutation polytopes of cyclic groups
In: Discrete Mathematics and Theoretical Computer Science, 2012, S. 421-432
2011
Begutachteter Zeitschriftenartikel
Examples of Kähler-Einstein toric Fano manifolds associated to non-symmetric reflexive polytopes
In: Beitrage zur Algebra und Geometrie, Vol. 52, 2011, Issue 2, S. 297-304, 10.1007/s13366-011-0041-y
Projecting lattice polytopes without interior lattice points
In: Mathematics of Operations Research, Vol. 36, 2011, Issue 3, S. 462-467, 10.1287/moor.1110.0503
2010
Begutachteter Zeitschriftenartikel
A simple combinatorial criterion for projective toric manifolds with dual defect
In: Mathematical Research Letters, Vol. 17, 2010, Issue 3, S. 435-448
On the combinatorial classification of toric log del {P}ezzo surfaces
In: LMS J. Comput. Math., Vol. 13, 2010, S. 33--46, ISSN 1461-1570, 10.1112/S1461157008000387
Q-Factorial gorenstein toric fano varieties with large picard number
In: Tohoku Mathematical Journal, Vol. 62, 2010, Issue 1, S. 1-15
2009
Begutachteter Zeitschriftenartikel
Cayley decompositions of lattice polytopes and upper bounds for h-polynomials
In: Journal fur die Reine und Angewandte Mathematik, 2009, Issue 637, S. 207-216, 10.1515/CRELLE.2009.096
Classification of toric Fano 5-folds
In: Advances in Geometry, Vol. 9, 2009, Issue 1, S. 85-97, 10.1515/ADVGEOM.2009.005
Flow polytopes and the graph of reflexive polytopes
In: Discrete Mathematics, Vol. 309, 2009, Issue 16, S. 4992-4999, 10.1016/j.disc.2009.03.001
On permutation polytopes
In: Advances in Mathematics, Vol. 222, 2009, Issue 2, S. 431-452, 10.1016/j.aim.2009.05.003
2008
Begutachteter Zeitschriftenartikel
A boundedness result for toric log Del Pezzo surfaces
In: Archiv der Mathematik, Vol. 91, 2008, Issue 6, S. 526-535, 10.1007/s00013-008-2913-4
Lattice points in Minkowski sums
In: Electronic Journal of Combinatorics, Vol. 15, 2008, Issue 1 N
Lattice polytopes having h*-polynomials with given degree and linear coefficient
In: European Journal of Combinatorics, Vol. 29, 2008, Issue 7, S. 1596-1602, 10.1016/j.ejc.2007.11.002
Lattices generated by skeletons of reflexive polytopes
In: Journal of Combinatorial Theory. Series A, Vol. 115, 2008, Issue 2, S. 340-344, 10.1016/j.jcta.2007.05.003
Stanley's conjecture, cover depth and extremal simplicial complexes
In: Matematiche (Catania), Vol. 63, 2008, Issue 2, S. 213--228 (2009), ISSN 0373-3505
Buchbeitrag
Combinatorial aspects of mirror symmetry
In: Vol. 452, 2008, S. 35--66, 10.1090/conm/452/08770
Let me tell you my favorite lattice-point problem {$\dots$}
In: Vol. 452, 2008, S. 179--187, 10.1090/conm/452/08782
2007
Begutachteter Zeitschriftenartikel
Multiples of lattice polytopes without interior lattice points
In: Mosc. Math. J., Vol. 7, 2007, Issue 2, S. 195--207, 349, ISSN 1609-3321
Volume and lattice points of reflexive simplices
In: Discrete and Computational Geometry, Vol. 37, 2007, Issue 2, S. 301-320, 10.1007/s00454-006-1299-y
2006
Begutachteter Zeitschriftenartikel
Complete toric varieties with reductive automorphism group
In: Mathematische Zeitschrift, Vol. 252, 2006, Issue 4, S. 767-786, 10.1007/s00209-005-0880-z
Buchbeitrag
Classification of pseudo-symmetric simplicial reflexive polytopes
In: Algebraic and geometric combinatorics : Euroconference in Mathematics, Algebraic and Geometric Combinatorics, August 20 - 26, 2005, Anogia, Crete, Greece. - Providence, RI : American Mathematical Society, S. 269-282, 2006
2005
Begutachteter Zeitschriftenartikel
Gorenstein toric Fano varieties
In: Manuscripta Mathematica, Vol. 116, 2005, Issue 2, S. 183-210, 10.1007/s00229-004-0532-3