Publikationen

2023

Begutachteter Zeitschriftenartikel

Thin polytopes - lattice polytopes with vanishing local h*-polynomial

Nill, Benjamin; Borger, Christopher; Kretschmer, Andreas

In: International mathematics research notices - Oxford : Oxford University Press . - 2023

2022

Buchbeitrag

Stability of tangent bundles on smooth toric Picard-rank-2 varieties and surfaces

Hering, Milena; Nill, Benjamin; Süß, Hendrik

In: Facets of algebraic geometry ; 2 - Cambridge: Cambridge University Press; Aluffi, Paolo *1960-* . - 2022, insges. 25 S.

Begutachteter Zeitschriftenartikel

On the maximum dual volume of a canonical Fano polytope

Nill, Benjamin; Baletti, Gabriele; Kasprzyk, Alexander M.

In: Forum of mathematics / Sigma - Cambridge : Cambridge Univ. Press, Bd. 10 (2022), Artikel e109, insges. 19 S.

2020

Begutachteter Zeitschriftenartikel

Gorenstein polytopes with trinomial h -polynomials

Higashitani, Akihiro; Nill, Benjamin; Tsuchiya, Akiyoshi

In: Beiträge zur Algebra und Geometrie - Berlin: Springer . - 2020[Online first]

Begutachteter Zeitschriftenartikel

The mixed degree of families of lattice polytopes

Nill, Benjamin

In: Annals of combinatorics - [Cham (ZG)]: [Springer International Publishing AG], Bd. 24 (2020), S. 203-216

Begutachteter Zeitschriftenartikel

On defectivity of families of full-dimensional point configurations

Borger, Christopher; Nill, Benjamin

In: Proceedings of the American Mathematical Society / B/ American Mathematical Society - Providence, RI: Soc., Bd. 7 (2020), S. 43-51

Dissertation

Mixed lattice polytope theory with a view towards sparse polynomial systems

Borger, Christopher; Nill, Benjamin

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

Di Rocco, Sandra; Haase, Christian; Nill, Benjamin

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

Averkov, Gennadiy; Hofscheier, Johannes; Nill, Benjamin

In: De.arxiv.org - [S.l.]: Arxiv.org, 1991, 2019, article 1911.03511, 11 Seiten

2018

Begutachteter Zeitschriftenartikel

Smooth polytopes with negative Ehrhart coefficients

Castillo, Federico; Liu, Fu; Nill, Benjamin; Paffenholz, Andreas

In: Journal of combinatorial theory / A - Amsterdam [u.a.]: Elsevier, 1971, Bd. 160.2018, S. 316-331

Begutachteter Zeitschriftenartikel

Lattice simplices with a fixed positive number of interior lattice points - a nearly optimal volume bound

Averkov, Gennadiy; Krümpelmann, Jan; Nill, Benjamin

In: International mathematics research notices: IMRN - Oxford: Oxford University Press, 1991 . - 2018[Online first]

Begutachteter Zeitschriftenartikel

On Ehrhart polynomials of lattice triangles

Hofscheier, Johannes; Nill, Benjamin; Öberg, Dennis

In: The electronic journal of combinatorics - [Madralin]: EMIS ELibEMS, 1994, Vol. 25.2018, 1, Art. P1.3, insgesamt 8 S.

Habilitation

Modern aspects of classical convex geometry

Saorín Gómez, Eugenia; Nill, Benjamin

In: Magdeburg, 2017, xxxii, 153 Seiten, Illustrationen, 30 cm[Literaturverzeichnis: Seite 131-136]

2017

Begutachteter Zeitschriftenartikel

Minimality and mutation-equivalence of polygons

Kasprzyk, Alexander; Nill, Benjamin; Prince, Thomas

In: Forum of mathematics / Sigma - Cambridge: Cambridge Univ. Press, Vol. 5.2017, Art. e18, insgesamt 48 S.

Begutachteter Zeitschriftenartikel

Ehrhart theory of spanning lattice polytopes

Hofscheier, Johannes; Katthän, Lukas; Nill, Benjamin

In: International mathematics research notices : IMRN - Oxford : Oxford University Press, 2017

2015

Begutachteter Zeitschriftenartikel

A bound for the splitting of smooth Fano polytopes with many vertices

Assarf, Benjamin; Nill, Benjamin

In: Journal of algebraic combinatorics - Dordrecht [u.a.]: Springer Science + Business Media B.V, 1992 . - 2015, insges. 20 S.

Begutachteter Zeitschriftenartikel

Finitely many smooth d-polytopes with n lattice points

Bogart, Tristram; Haase, Christian; Hering, Milena; Lorenz, Benjamin; Nill, Benjamin; Paffenholz, Andreas; Rote, Günter; Santos, Francisco; Schenck, Hal

In: Israel journal of mathematics - Berlin: Springer, Bd. 207 (2015), 1, S. 301-329

Begutachteter Zeitschriftenartikel

Largest integral simplices with one interior integral point - solution of Hensley's conjecture and related results

Averkov, Gennadiy; Krümpelmann, Jan; Nill, Benjamin

In: Advances in mathematics - Amsterdam [u.a.]: Elsevier, 1961, Bd. 274.2015, S. 118-166, 2014

Begutachteter Zeitschriftenartikel

On smooth {G}orenstein polytopes

Lorenz, Benjamin; Nill, Benjamin

In: Tohoku Math. J. (2), Vol. 67, 2015, Issue 4, S. 513--530, ISSN 0040-8735, 10.2748/tmj/1450798070

Begutachteter Zeitschriftenartikel

The degree of point configurations - Ehrhart theory, Tverberg points and almost neighborly polytopes

Nill, Benjamin; Padrol, Arnau

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

Nill, B.; Paffenholz, A.

In: Advances in Geometry, Vol. 14, 2014, Issue 4, S. 579-586, 10.1515/advgeom-2014-0001

Begutachteter Zeitschriftenartikel

Polytopes associated to dihedral groups

Baumeister, B.; Haase, C.; Nill, B.; Paffenholz, A.

In: Ars Mathematica Contemporanea, Vol. 7, 2014, Issue 1, S. 30-38

2013

Buchbeitrag

Fano polytopes

Kasprzyk, Alexander M.; Nill, Benjamin

In: 2013, S. 349--364

Begutachteter Zeitschriftenartikel

Polyhedral adjunction theory

Di Rocco, S.; Haase, C.; Nill, B.; Paffenholz, A.

In: Algebra and Number Theory, Vol. 7, 2013, Issue 10, S. 2417-2446, 10.2140/ant.2013.7.2417

Begutachteter Zeitschriftenartikel

Gorenstein polytopes and their stringy E-functions

Nill, B.; Schepers, J.

In: Mathematische Annalen, Vol. 355, 2013, Issue 2, S. 457-480, 10.1007/s00208-012-0792-2

2012

Buchbeitrag

Permutation polytopes of cyclic groups

Baumeister, B.; Haase, C.; Nill, B.; Paffenholz, A.

In: Discrete Mathematics and Theoretical Computer Science, 2012, S. 421-432

Begutachteter Zeitschriftenartikel

Reflexive polytopes of higher index and the number 12

Kasprzyk, A.M.; Nill, B.

In: Electronic Journal of Combinatorics, Vol. 19, 2012, Issue 3, S. 1-18

Begutachteter Zeitschriftenartikel

Lattice-width directions and minkowski's 3 d-theorem

Draisma, J.; McAllister, T.B.; Nill, B.

In: SIAM Journal on Discrete Mathematics, Vol. 26, 2012, Issue 3, S. 1104-1107, 10.1137/120877635

Begutachteter Zeitschriftenartikel

A relation between number of integral points, volumes of faces and degree of the discriminant of smooth lattice polytopes

Dickenstein, A.; Nill, B.; Vergne, M.

In: Comptes Rendus Mathematique, Vol. 350, 2012, Issue 5-6, S. 229-233, 10.1016/j.crma.2012.02.001

2011

Begutachteter Zeitschriftenartikel

Examples of Kähler-Einstein toric Fano manifolds associated to non-symmetric reflexive polytopes

Nill, B.; Paffenholz, A.

In: Beitrage zur Algebra und Geometrie, Vol. 52, 2011, Issue 2, S. 297-304, 10.1007/s13366-011-0041-y

Begutachteter Zeitschriftenartikel

Projecting lattice polytopes without interior lattice points

Nill, B.; Ziegler, G.M.

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

Dickenstein, A.; Nill, B.

In: Mathematical Research Letters, Vol. 17, 2010, Issue 3, S. 435-448

Begutachteter Zeitschriftenartikel

Q-Factorial gorenstein toric fano varieties with large picard number

Nill, B.; Øbro, M.

In: Tohoku Mathematical Journal, Vol. 62, 2010, Issue 1, S. 1-15

Begutachteter Zeitschriftenartikel

On the combinatorial classification of toric log del {P}ezzo surfaces

Kasprzyk, Alexander M.; Kreuzer, Maximilian; Nill, Benjamin

In: LMS J. Comput. Math., Vol. 13, 2010, S. 33--46, ISSN 1461-1570, 10.1112/S1461157008000387

2009

Begutachteter Zeitschriftenartikel

Classification of toric Fano 5-folds

Kreuzer, M.; Nill, B.

In: Advances in Geometry, Vol. 9, 2009, Issue 1, S. 85-97, 10.1515/ADVGEOM.2009.005

Begutachteter Zeitschriftenartikel

On permutation polytopes

Baumeister, B.; Haase, C.; Nill, B.; Paffenholz, A.

In: Advances in Mathematics, Vol. 222, 2009, Issue 2, S. 431-452, 10.1016/j.aim.2009.05.003

Begutachteter Zeitschriftenartikel

Cayley decompositions of lattice polytopes and upper bounds for h-polynomials

Haase, C.; Nill, B.; Payne, S.

In: Journal fur die Reine und Angewandte Mathematik, 2009, Issue 637, S. 207-216, 10.1515/CRELLE.2009.096

Begutachteter Zeitschriftenartikel

Flow polytopes and the graph of reflexive polytopes

Altmann, K.; Nill, B.; Schwentner, S.; Wiercinska, I.

In: Discrete Mathematics, Vol. 309, 2009, Issue 16, S. 4992-4999, 10.1016/j.disc.2009.03.001

2008

Buchbeitrag

Let me tell you my favorite lattice-point problem {$\dots$}

Beck, Matthias; Nill, Benjamin; Reznick, Bruce; Savage, Carla; Soprunov, Ivan; Xu, Zhiqiang

In: Vol. 452, 2008, S. 179--187, 10.1090/conm/452/08782

Buchbeitrag

Combinatorial aspects of mirror symmetry

Batyrev, Victor; Nill, Benjamin

In: Vol. 452, 2008, S. 35--66, 10.1090/conm/452/08770

Begutachteter Zeitschriftenartikel

A boundedness result for toric log Del Pezzo surfaces

Dais, D.I.; Nill, B.

In: Archiv der Mathematik, Vol. 91, 2008, Issue 6, S. 526-535, 10.1007/s00013-008-2913-4

Begutachteter Zeitschriftenartikel

Stanley's conjecture, cover depth and extremal simplicial complexes

Nill, Benjamin; Vorwerk, Kathrin

In: Matematiche (Catania), Vol. 63, 2008, Issue 2, S. 213--228 (2009), ISSN 0373-3505

Begutachteter Zeitschriftenartikel

Lattices generated by skeletons of reflexive polytopes

Haase, C.; Nill, B.

In: Journal of Combinatorial Theory. Series A, Vol. 115, 2008, Issue 2, S. 340-344, 10.1016/j.jcta.2007.05.003

Begutachteter Zeitschriftenartikel

Lattice points in Minkowski sums

Haase, C.; Nill, B.; Paffenholz, A.; Santos, F.

In: Electronic Journal of Combinatorics, Vol. 15, 2008, Issue 1 N

Begutachteter Zeitschriftenartikel

Lattice polytopes having h*-polynomials with given degree and linear coefficient

Nill, B.

In: European Journal of Combinatorics, Vol. 29, 2008, Issue 7, S. 1596-1602, 10.1016/j.ejc.2007.11.002

2007

Begutachteter Zeitschriftenartikel

Multiples of lattice polytopes without interior lattice points

Batyrev, Victor; Nill, Benjamin

In: Mosc. Math. J., Vol. 7, 2007, Issue 2, S. 195--207, 349, ISSN 1609-3321

Begutachteter Zeitschriftenartikel

Volume and lattice points of reflexive simplices

Nill, B.

In: Discrete and Computational Geometry, Vol. 37, 2007, Issue 2, S. 301-320, 10.1007/s00454-006-1299-y

2006

Buchbeitrag

Classification of pseudo-symmetric simplicial reflexive polytopes

Nill, Benjamin

In: Algebraic and geometric combinatorics - Euroconference in Mathematics, Algebraic and Geometric Combinatorics, August 20 - 26, 2005, Anogia, Crete, Greece: Euroconference in Mathematics, Algebraic and Geometric Combinatorics, August 20 - 26, 2005, Anogia, Crete, Greece/ Euroconference Algebraic and Geometric Combinatorics - Providence, RI: American Mathematical Society . - 2006, S. 269-282

Begutachteter Zeitschriftenartikel

Complete toric varieties with reductive automorphism group

Nill, B.

In: Mathematische Zeitschrift, Vol. 252, 2006, Issue 4, S. 767-786, 10.1007/s00209-005-0880-z

2005

Begutachteter Zeitschriftenartikel

Gorenstein toric Fano varieties

Nill, B.

In: Manuscripta Mathematica, Vol. 116, 2005, Issue 2, S. 183-210, 10.1007/s00229-004-0532-3

Letzte Änderung: 08.06.2023 - Ansprechpartner: Webmaster