under construction

on lattice width of lattice-free polyhedra and height of Hilbert bases
jointly with Stefan Kuhlmann and Robert Weismantel

arXiv:2110.02893

arXiv:2110.02893

proximity bounds for random integer programs
jointly with Marcel Celaya

Preprint 05-2020 TU Berlin, 2020

Preprint 05-2020 TU Berlin, 2020

packing minima and lattice points in convex bodies
jointly with Matthias Schymura and Fei Xue

to appear in Moscow Journal of Combinatorics and Number Theory; arXiv:2005.02234

to appear in Moscow Journal of Combinatorics and Number Theory; arXiv:2005.02234

distance-sparsity transference for vertices of corner polyhedra
jointly with Iskander Aliev, Marcel Celaya, and Aled Williams

SIAM J. Optim. 2021, 31(1), 2021, 200--216; arXiv:2007.00950

SIAM J. Optim. 2021, 31(1), 2021, 200--216; arXiv:2007.00950

bounds on the lattice point enumerator via slices and projections
jointly with Ansgar Freyer

to appear in Discrete Comput. Geom.; arXiv:2004.14097

to appear in Discrete Comput. Geom.; arXiv:2004.14097

packings, sausages and catastrophes
jointly with Jörg M. Wills

to appear Beiträge zur Algbera und Geometrie preprint tu berlin-04/2020; (open access)

to appear Beiträge zur Algbera und Geometrie preprint tu berlin-04/2020; (open access)

discrete analogues of John’s theorem
jointly with Sören Berg

Moscow Journal of Combinatorics and Number Theory 8-4 (2019), 367-378; arxiv:1809.08943

Moscow Journal of Combinatorics and Number Theory 8-4 (2019), 367-378; arxiv:1809.08943

on successive minima-type inequalities for the polar of a convex body
jointly with Fei Xue

Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 113 (2019), no. 3, 2601–2616; arxiv:1809.08943

Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 113 (2019), no. 3, 2601–2616; arxiv:1809.08943

distances to lattice points in knapsack polyhedra
jointly with Iskander Aliev and Timm Oertel

Math. Programming Series A 182 (2020), 175–-198; arxiv:1805.04592

Math. Programming Series A 182 (2020), 175–-198; arxiv:1805.04592

a characterization of dual quermassintegrals and the roots of dual steiner polynomials
jointly with David Alonso-Gutiérrez and María A. Hernández Cifre

Adv. Math. 331 (20), 2018, 565-588; arXiv:1707.01675

Adv. Math. 331 (20), 2018, 565-588; arXiv:1707.01675

on the the log-minkowski inequality
for simplices and parallelepipeds
jointly with Hannes Pollehn

Acta Math. Hungar. 155 (1), 2018, 141-157.

Acta Math. Hungar. 155 (1), 2018, 141-157.

necessary subspace concentration conditions for the even dual minkowski problem
jointly with Hannes Pollehn

Adv. Math. 323, 2018, 114-141 temporary access; arXiv:1703.10528

Adv. Math. 323, 2018, 114-141 temporary access; arXiv:1703.10528

a note on lattice packings via lattice refinements
Experimental Mathematics 27(1), 2018, 1-9; preprint tu berlin,
update

subspace concentration of dual curvature measures
jointly with Károly Böröczky and Hannes Pollehn

J. Differential Geometry 109(3), 2018, 411--429; arXiv:1604.07390

J. Differential Geometry 109(3), 2018, 411--429; arXiv:1604.07390

integrality gaps of integer knapsack problems
jointly with Iskander Aliev and Timm Oertel

IPCO 2017, Waterloo, ON, Canada, June 26-28, 2017, Proceedings, 25-38; arXiv:1611.03768

IPCO 2017, Waterloo, ON, Canada, June 26-28, 2017, Proceedings, 25-38; arXiv:1611.03768

cone-volume measure and stability
jointly with Károly J. Böröczky

Adv. Math. 306, 2017, 24-50; arXiv:1407.7272

Adv. Math. 306, 2017, 24-50; arXiv:1407.7272

a discrete version of koldobsky's slicing inequality
jointly with Matthew Alexander and Artem Zvavitch

Israel J. Math. 222(1), 2017, 261–278; arXiv:1511.02702

Israel J. Math. 222(1), 2017, 261–278; arXiv:1511.02702

lattice point inequalities for centered convex bodies
jointly with Sören Lennart Berg

SIAM J Discrete Math 30(2), 2016, 1148–1158; arXiv:1505.06444

SIAM J Discrete Math 30(2), 2016, 1148–1158; arXiv:1505.06444

cone-volume measure of general centered convex bodies
jointly with Károly J. Böröczky

Adv. Math., 286, 2016, 703-721.

Adv. Math., 286, 2016, 703-721.

note on adelic triangulations and an adelic blichfeldt-type inequality
jointly with Carsten Thiel

Beiträge Algebra Geom., 57, 2016, 37–49; arXiv:1405.5798

Beiträge Algebra Geom., 57, 2016, 37–49; arXiv:1405.5798

on extensions of minkowski's theorem on successive minima
jointly with Matthias Henze and Maria Hernandez Cifre

Forum Math., 28(2), 2016, 311-326; arXiv:1405.4993

Forum Math., 28(2), 2016, 311-326; arXiv:1405.4993

note on the coefficients of rational
ehrhart quasi-polynomials of minkowski sums
jointly with Eva Linke

Online J. Anal. Comb. (10), 2015; pdf

Online J. Anal. Comb. (10), 2015; pdf

cone-volume measures of polytopes
jointly with Eva Linke

Adv. Math., 253, 2014, 50-62; arXiv:1305.5335

Adv. Math., 253, 2014, 50-62; arXiv:1305.5335

restricted successive minima
jointly with Carsten Thiel

Pacific J. Math., 269(2), 2014, 341-354; arXiv:1302.1407v2

Pacific J. Math., 269(2), 2014, 341-354; arXiv:1302.1407v2

integer points in knapsack polytopes and s-covering radius
jointly with Iskander Aliev and Eva Linke

The Electronic Journal of Combinatorics, 20(2) (2013), #P42, arXiv:1211.3269

The Electronic Journal of Combinatorics, 20(2) (2013), #P42, arXiv:1211.3269

löwner-john ellipsoids
Doc. Math., Extra Volume ISMP (2012) 95-106;
peprint uni magdeburg

steiner polynomials via ultra-logconcave sequences
jointly with Maria A. Hernandez Cifre and Eugenia Saorin

Commun. Contemp. Math. 14(6), 2012, arXiv:1112.4741v1

Commun. Contemp. Math. 14(6), 2012, arXiv:1112.4741v1

lll-reduction for integer knapsacks
jointly with Iskander Aliev

J. Comb. Optim. 24(4), 2012, 613-626; arxiv:1012.3182

J. Comb. Optim. 24(4), 2012, 613-626; arxiv:1012.3182

blichfeldt-type inequalities and central symmetry
jointly with Matthias Henze and Jörg M. Wills

Adv. Geom. 11(4), 2011, 731-744; preprint uni magdeburg

Adv. Geom. 11(4), 2011, 731-744; preprint uni magdeburg

generalized frobenius numbers: bounds and average behavior
jointly with Iskander Aliev and Lenny Fukshansky

Acta Arith. 155, (2012), 53-62; arxiv:1105.0841

Acta Arith. 155, (2012), 53-62; arxiv:1105.0841

notes on lattice points of zonotopes and lattice-face polytopes
jointly with Christian Bey, Matthias Henze and Eva Linke

Discrete Math. 311, 2011, 634-644; arxiv:1006.5574v2

Discrete Math. 311, 2011, 634-644; arxiv:1006.5574v2

on the location of roots of steiner polynomials
jointly with Maria A. Hernandez Cifre

Bull. Braz. Math. Soc., New Series 42 (1), 2011, 153-170, preprint uni magdeburg

Bull. Braz. Math. Soc., New Series 42 (1), 2011, 153-170, preprint uni magdeburg

representing simple d-dimensional polytopes by d polynomials
jointly with Gennadiy Averkov

Math. Prog. (A),

Math. Prog. (A),

**126**(2), 2011, 203-230; arXiv:0709.2099v1
feasability of integer knapsacks
jointly with Iskander Aliev

SIAM Journal on Optimization 20 (2010), issue 6, 2978-2993; pdf

SIAM Journal on Optimization 20 (2010), issue 6, 2978-2993; pdf

minimal zonotopes containing the crosspolytope
jointly with Eva Linke and Jörg M. Wills

Linear Algebra and its Applications 432 (2010), 2942-2952; preprint 2009/41 uni magdeburg

Linear Algebra and its Applications 432 (2010), 2942-2952; preprint 2009/41 uni magdeburg

expected frobenius numbers
jointly with Iskander Aliev and Aicke Hinrichs

Journal of Combinatorial Theory, Series A, 118 (2011), 525 - 531; arxiv:0910.02620

Journal of Combinatorial Theory, Series A, 118 (2011), 525 - 531; arxiv:0910.02620

coverings and compressed lattices
jointly with Maria A. Hernandez Cifre

Symmetry: Culture and Science,

Symmetry: Culture and Science,

**22**(3-4), 2011, 307-316; preprint 2009/39 uni magdeburg
integer knapsacks: average behavior of the frobenius numbers
jointly with Iskander Aliev

Mathematics of Operations Research,

Mathematics of Operations Research,

**34**(3), 2009, 698-705; arxiv:0810.0234v1
three-dimensional polyhedra can be described by three polynomial inequalities
jointly with Gennadiy Averkov

Discrete Comput. Geom.,

Discrete Comput. Geom.,

**42**(2), 2009, 166-186; arXiv:0807.2137
successive minima and radii
jointly with Maria A. Hernandez Cifre

Canad. Math. Bull.,

Canad. Math. Bull.,

**52**(3), 2009, 380-388; preprint 02/2008 uni magdeburg
lower bounds on the coefficients of ehrhart polynomials
jointly with Makoto Tagami

European J. Combinat.,

European J. Combinat.,

**30**, 2009, 70-83; arXiv:0710.2665v1
intrinsic volumes and successive radii
jointly with Maria A. Hernandez Cifre

J. Math. Anal. Appl.,

J. Math. Anal. Appl.,

**343**(2), 2008, 733-742; preprint 29/2007 uni magdeburg
a blichfeldt-type inequality for the surface area
jointly with Jörg M. Wills

Mh. Math.,

Mh. Math.,

**154**, 2008, 135-144; arXiv:0705.2088v1
notes on the roots of steiner polynomials
jointly with Maria A. Hernandez Cifre

Rev. Mat. Iberoamericana,

Rev. Mat. Iberoamericana,

**24**(2), 2008, 631-644; arXiv:math.MG/0703373
polynomdarstellungen von polyedern (german)
Jahresberichte der DMV,

**109**, 2007, 51-69; preprint 58/2006 uni magdeburg
notes on the roots of ehrhart polynomials
jointly with Christian Bey and Jörg M. Wills

Discrete Comput. Geom.,

Discrete Comput. Geom.,

**38**(1), 2007, 81-98; arXiv:math.MG/0606089
minkowski's successive minima
jointly with Jörg M. Wills

Proceedings of ''The International Conference on Number Theory and Discrete Geometry'', Chandigarh, 2005; Editors: R. Balasubramanian, S.G. Dani, P.M. Gruber, R.J. Hans-Gill; Ramanujan Mathematical Society, 2008, 129-142; preprint 09/2006 uni magdeburg

Proceedings of ''The International Conference on Number Theory and Discrete Geometry'', Chandigarh, 2005; Editors: R. Balasubramanian, S.G. Dani, P.M. Gruber, R.J. Hans-Gill; Ramanujan Mathematical Society, 2008, 129-142; preprint 09/2006 uni magdeburg

on the existence of crepant resolutions of gorenstein abelian quotient singularities in dimensions >= 4
jointly with Dimitrios I. Dais and Günter M. Ziegler

Algebraic and Geometric Combinatorics (Athanasiadis et al., eds.), Contemp. Math. (AMS),

Algebraic and Geometric Combinatorics (Athanasiadis et al., eds.), Contemp. Math. (AMS),

**423**, 2007, 125-193; arXiv:math.AG/0512619
lattice point coverings
jointly with George Tsintsifas

Chinese Advances in Mathematics,

Chinese Advances in Mathematics,

**36**(4), 2007, 441-446. preprint 29/2005 uni magdeburg
successive minima and best simultaneous diophantine approximations
jointly with Iskander Aliev

Mh. Math.,

Mh. Math.,

**147**(2), 2006, 95-101; arXiv:math.NT/0503365
ehrhart polynomials and successive minima
jointly with Achill Schürmann and Jörg M. Wills

Mathematika,

Mathematika,

**52**(103/104), 2006, 1-16; arXiv:math.AG/0507528
polynomial inequalities representing polyhedra
jointly with Hartwig Bosse and Martin Grötschel

Math. Prog. (A),

Math. Prog. (A),

**103**:1, 2005, 35-44; arXiv:math.MG/0307190
on the equations defining toric l.c.i. singularities
jointly with Dimitrios I. Dais

Trans. Amer. Math.

Trans. Amer. Math.

**535**(12), 2003, 4955 - 4984; arXiv:math.AG/0204172
on the representation of polyhedra by polynomial inequalities
jointly with Martin Grötschel

Discrete Comput. Geom.

Discrete Comput. Geom.

**29**(4), 2003, 485 - 504; arXiv:math.MG/0203268
integral decomposition of polyhedra and some applications
in mixed integer programming
jointly with Matthias Köppe and Robert Weismantel

Math. Prog. (B).

Math. Prog. (B).

**94**, 2003, 193-206; preprint 12/2000 uni magdeburg
successive minima and lattice points
Rendi. Circ. Matematico Palermo, Serie II, Supppl.

**70**, 2002, 377-384; arXiv:math.MG/0204158
diophantine approximations and integer points of cones
jointly with Robert Weismantel

Combinatorica,

Combinatorica,

**22**(3), 2002, 401 - 408; preprint 29/97 zuse zentrum berlin
on free planes in lattice ball packings
jointly with Günter M. Ziegler and Chuanming Zong

London Math. Soc.

London Math. Soc.

**34**, no. 3, 2002, 284-290; preprint 04/2000 uni magdeburg
die starke-perfekte-graphen-vermutung (german)
jointly with Annegret Wagler

DMV-Mitteilungen

DMV-Mitteilungen

**3**, 2002, 22-25; preprint
segments in ball packings
jointly with Chuanming Zong

Mathematika

Mathematika

**47**, 2000, 31-38; preprint 30/1999 uni magdeburg
densest lattice packings of 3-polytopes
jointly with Ulrich Betke

Computational Geometry

Computational Geometry

**16**, no. 3, 2000, 157-186; arXiv:math.MG/9909172
on minimal solutions of linear diophantine equations
jointly with Robert Weismantel

Contrib. Algebra and Geometry

Contrib. Algebra and Geometry

**41**, (1), 2000, 49-55; preprint 02/1999 uni magdeburg
kugeln im computer - die kepler vermutung (german)
jointly with Günter M. Ziegler

in

in

*Alles Mathematik!*, M. Aigner and E. Behrends eds., 2nd ed., Vieweg, 2002; preprint
la congettura di keplero (italian)
in *Problemi e
teoremi, volume II*, C. Bartocci and P. Odifreddi,
Eiaudi, Torino, 2008;

spheres in the computer -- the
kepler conjecture (english)
in *Mathematics Everywhere*, M. Aigner and
E. Behrends eds., AMS, 2010

a counterexample to an integer analogue of carathéodory's
theorem
jointly with Winfried Bruns, Joseph Gubeladze, Alexander Martin and Robert Weismantel

J. Reine Angew. Math.

J. Reine Angew. Math.

**510**, 1999, 179-185; preprint sc 98-28 zib
random projections of regular polytopes
jointly with Károly Böröczky, Jr.

Arch. Math.

Arch. Math.

**73**, 1999, 465-473; preprint sc 97-21 zib
all abelian quotient c.i.-singularities admit
projective crepant resolutions in all dimensions
jointly with Dimitrios I. Dais and Günter M. Ziegler

Advances in Mathematics

Advances in Mathematics

**139**, 1998, 194-239; arXiv:alg-geom/9704007
on crepant resolutions of 2-parameter series of gorenstein cyclic quotient singularities
jointly with Dimitrios I. Dais and Utz-Uwe Haus

Results in Mathematics

Results in Mathematics

**33**, No. 3/4, 1998, 208-266; arXiv:math.AG/9803096
randomized simplex algorithms on klee-minty cubes
jointly with Bernd Gärtner and Günter M. Ziegler;

Combinatorica

Combinatorica

**18**(3), 1998, 349-372; preprint
finite packings of spheres
jointly with Ulrich Betke

Discrete Comput. Geom.

Discrete Comput. Geom.

**19**, 1998 , 197-227; preprint 465-1995 tu berlin
note on lattice-point-free convex bodies
jointly with Poh Wah Awyong and Paul R. Scott

Mh. Math.

Mh. Math.

**126**, 1998, 7-12; preprint sc-96-44 zib
test sets of the knapsack problem and simultaneous diophantine approximatio
jointly with Robert Weismantel

Lecture Notes in Comp. Science 1284, Algorithms -ESA'97, R. Burkard and G. Woeginger eds., Springer, 1997, 271-283; preprint sc-97-13 zib

Lecture Notes in Comp. Science 1284, Algorithms -ESA'97, R. Burkard and G. Woeginger eds., Springer, 1997, 271-283; preprint sc-97-13 zib

the height of minimal hilbert bases
jointly with Robert Weismantel

Results in Mathemtics,

Results in Mathemtics,

**32**, 1997, 298-303; preprint
note on shortest and nearest lattice vectors
Inform. Process. Lett.,

**61**, 1997, 183-188; preprint 430-1995 tu berlin
inradii of simplices
jointly with Ulrich Betke and Lydia Tsintsifa

Discrete Comput. Geom.,

Discrete Comput. Geom.,

**17**, 1997, 365-375; preprint
basic properties of convex polytopes
jointly with Jürgen Richter-Gebert and Günter
M. Ziegler

Discrete and Computational Geometry, J.E. Goodman and J. O'Rourke eds., CRC Press, Boca Raton, Florida, 1997, Second Edition, 2004, 355-383; preprint 473-1995 tu berlin with updates

Discrete and Computational Geometry, J.E. Goodman and J. O'Rourke eds., CRC Press, Boca Raton, Florida, 1997, Second Edition, 2004, 355-383; preprint 473-1995 tu berlin with updates

radii and the sausage conjecture
jointly with Károly Böröczky, Jr.

Canad. Math. Bull.

Canad. Math. Bull.

**38**(2), 1995, 156-166;
finite and infinite packings
Habilitationsschrift, Universität Siegen, 1995; preprint

a new approach to covering
jointly with Ulrich Betke and Jörg M. Wills

Mathematika,

Mathematika,

**42**, 1995, 251-263; preprint 266-1994 uni siegen
sausages are good packings
jointly with Ulrich Betke and Jörg M. Wills

Discrete Comput. Geom.,

Discrete Comput. Geom.,

**13**, 1995, 297-311;
finite and infinite packings
jointly with Ulrich Betke and Jörg M. Wills

J. Reine Angew. Math.,

J. Reine Angew. Math.,

**453**, 1994, 165-191; preprint 262-1993 uni siegen
some inequalities for planar convex figures
jointly with George A. Tsintsifas

El. Math.,

El. Math.,

**49**(3), 1994, 120-126; preprint
intrinsic volumes and lattice points of
crosspolytopes
jointly with Ulrich Betke

Mh. Math.

Mh. Math.

**115**, 1993, 27-33; preprint 1992 uni siegen
successive-minima-type inequalities
jointly with Ulrich Betke and Jörg M. Wills

Discrete Comput. Geom.,

Discrete Comput. Geom.,

**9**, 1993, 165-175; preprint 1992 uni siegen
a generalization of steinhagen's theorem
jointly with Ulrich Betke

Abh. Math. Sem. Univ. Hamburg,

Abh. Math. Sem. Univ. Hamburg,

**63**, 1993, 165-176; preprint 259-1992 uni siegen
approximating the volume of convex bodies
jointly with Ulrich Betke

Discrete Comput. Geom.

Discrete Comput. Geom.

**10**, 1993, 15-21; preprint uni siegen
estimating sizes of a convex body by
successive diameters and widths
jointly with Ulrich Betke

Mathematika

Mathematika

**39**, 1992, 247-257; preprint 251/1991 uni siegen
ungleichungen für sukzessive minima und
verallgemeinerte in- und umkugelradien
Dissertation, Universität Siegen, 1991;
preprint

linear programming by minimizing distances
jointly with Ulrich Betke

ZOR-Methods and Models of OR,

ZOR-Methods and Models of OR,

**35**, 1991, 299-307.
inequalities between successive minima and intrinsic
volumes of a convex body
Mh. Math.,

**110**, 1990, 279-282.
ein polynomialer algorithmus zur lösung von linearen
optimierungsproblemen mit effizientem abbruchkriterium
Diplomarbeit, Universität Siegen, 1988.

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