My research interests are in polyhedral geometry, computational methods, and its connections with various other fields like (algebraic) combinatorics, algebraic geometry and convex optimization.

In particular I work on questions about lattice polytopes, their structure and classifications of subfamilies. For more see my preprints and slides of some talks.

My publications according to Zentralblatt, ORCID, and arXiv.

Preprints

(1)

Permutation Polytopes of Cyclic Groups

Preprint, TU Darmstadt, September 2011, 15 pages

Preprint, TU Darmstadt, September 2011, 15 pages

[arxiv]

Publications

(2)

Existence of regular unimodular triangulations --- Positive Results

Preprint, FU Berlin, June 2021, 96 pages

Appeared in: Memoirs of the AMS, 270 (2021), no. 1321, 96 pages

Preprint, FU Berlin, June 2021, 96 pages

Appeared in: Memoirs of the AMS, 270 (2021), no. 1321, 96 pages

(3)

Smooth Polytopes with negative Ehrhart Coefficients

Preprint, TU Darmstadt, November 2018, 16 pages

to appear in: Journal of Combinatorial Theory, Series A

Preprint, TU Darmstadt, November 2018, 16 pages

to appear in: Journal of Combinatorial Theory, Series A

(4)

polyDB - A database for polytopes and related objects

Preprint, TU Darmstadt, November 2017, 14 pages

Appeared in: Algorithmic and experimental methods in algebra, geometry, and number theory , Proceedings, Gebhard Böckle, Wolfram Decker and Gunter Malle (eds.), Springer 2017, pp. 533 - 547

Preprint, TU Darmstadt, November 2017, 14 pages

Appeared in: Algorithmic and experimental methods in algebra, geometry, and number theory , Proceedings, Gebhard Böckle, Wolfram Decker and Gunter Malle (eds.), Springer 2017, pp. 533 - 547

(5)

Toric Geometry in Polymake

Preprint, TU Darmstadt, June 2017, 4 pages

Appeared in: ACM Communications in Computer Algebra, 51 (2017), no. 3, pp. 92 - 94

Preprint, TU Darmstadt, June 2017, 4 pages

Appeared in: ACM Communications in Computer Algebra, 51 (2017), no. 3, pp. 92 - 94

(6)

Computing convex hulls and counting integer points with polymake

Preprint, TU Darmstadt, August 2014, 31 pages

Appeared in: Mathematical Programming Computation, 9 (2017), no. 1, pp. 1 - 38

Preprint, TU Darmstadt, August 2014, 31 pages

Appeared in: Mathematical Programming Computation, 9 (2017), no. 1, pp. 1 - 38

(7)

(8)

Finitely many smooth d-polytopes with n lattice points

Preprint, FU Berlin, October 2010, 24 pages

Appeared in: Israel J. Mathematics, 143 (2015), no. 11, pp. 4863 - 4873

Preprint, FU Berlin, October 2010, 24 pages

Appeared in: Israel J. Mathematics, 143 (2015), no. 11, pp. 4863 - 4873

(9)

Faces of Birkhoff Polytopes

Preprint, TU Darmstadt, April 2013, 29 pages

Appeared in: Electronic Journal of Combinatorics, 22 (2015), pp. #P1.67

Preprint, TU Darmstadt, April 2013, 29 pages

Appeared in: Electronic Journal of Combinatorics, 22 (2015), pp. #P1.67

(10)

Smooth Fano Polytopes with Many Vertices

Preprint, TU Darmstadt, September 2014, 36 pages

Appeared in: Discrete and Computational Geometry, 52 (2014), no. 2, pp. 153 - 194

Preprint, TU Darmstadt, September 2014, 36 pages

Appeared in: Discrete and Computational Geometry, 52 (2014), no. 2, pp. 153 - 194

(11)

On the equality case in Ehrhart's volume conjecture

Preprint, TU Darmstadt, May 2012, 6 pages

Appeared in: Advances in Geometry, 14 (2014), no. 4, pp. 579 - 586

Preprint, TU Darmstadt, May 2012, 6 pages

Appeared in: Advances in Geometry, 14 (2014), no. 4, pp. 579 - 586

(12)

Polytopes Associated to Dihedral Groups

Preprint, TU Darmstadt, August 2011, 9 pages

Appeared in: Ars Mathematica Contemporanea, 7 (2014), no. 1, pp. 30 - 38

Preprint, TU Darmstadt, August 2011, 9 pages

Appeared in: Ars Mathematica Contemporanea, 7 (2014), no. 1, pp. 30 - 38

(13)

Polyhedral Adjunction Theory

Preprint, Mittag-Leffler-Report, May 2011, 25 pages

Appeared in: Algebra and Number Theory, 7 (2013), no. 10, pp. 2417 - 2446

Preprint, Mittag-Leffler-Report, May 2011, 25 pages

Appeared in: Algebra and Number Theory, 7 (2013), no. 10, pp. 2417 - 2446

(14)

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

Preprint, FU Berlin, May 2009, 7 pages

Appeared in: Beiträge zur Algebra und Geometrie, 2 (2011), no. 2, pp. 297 - 304

Preprint, FU Berlin, May 2009, 7 pages

Appeared in: Beiträge zur Algebra und Geometrie, 2 (2011), no. 2, pp. 297 - 304

(15)

Lattice Points in Minkowski Sums

Preprint, FU Berlin, September 2007, 9 pages

Appeared in: Electronic Journal of Combinatorics, 15 (2008), no. N11, pp. #N11

Preprint, FU Berlin, September 2007, 9 pages

Appeared in: Electronic Journal of Combinatorics, 15 (2008), no. N11, pp. #N11

(16)

On Fanos and Chimneys

Preprint, FU Berlin, September 2007, 3 pages

Appeared in: Oberwolfach Reports, Report 39/2007 (2007), pp. 2303 - 2306

Preprint, FU Berlin, September 2007, 3 pages

Appeared in: Oberwolfach Reports, Report 39/2007 (2007), pp. 2303 - 2306

[journal]

(17)

On Permutation Polytopes

Preprint, FU Berlin, September 2009, 22 pages

Appeared in: Advances in Mathematics, 22 (2009), no. 2, pp. 431-452

Preprint, FU Berlin, September 2009, 22 pages

Appeared in: Advances in Mathematics, 22 (2009), no. 2, pp. 431-452

(18)

Quadratic Gröbner Bases for Smooth 3x3 Transportation Polytopes

Preprint, FU Berlin, June 2011, 6 pages

Appeared in: Journal of Algebraic Combinatorics, 30 (2009), no. 4, pp. 477 - 489

Preprint, FU Berlin, June 2011, 6 pages

Appeared in: Journal of Algebraic Combinatorics, 30 (2009), no. 4, pp. 477 - 489

(19)

Constructions for 4-Polytopes and the Cone of Flag Vectors

Preprint, FU Berlin, November 2005, 20 pages

Appeared in: Contemporary Mathematics, 423 (2006), pp. 283 - 303

Preprint, FU Berlin, November 2005, 20 pages

Appeared in: Contemporary Mathematics, 423 (2006), pp. 283 - 303

(20)

New polytopes from products

Preprint, TU Berlin, December 2005, 23 pages

Appeared in: Journal of Combinatorial Theory, Series A, 113 (2006), pp. 1396 - 1418

Preprint, TU Berlin, December 2005, 23 pages

Appeared in: Journal of Combinatorial Theory, Series A, 113 (2006), pp. 1396 - 1418

(21)

Bier spheres and posets

Preprint, TU Berlin, November 2003, 15 pages

Appeared in: Discrete and Computational Geometry, 34 (2005), no. 1, pp. 71 - 86

Preprint, TU Berlin, November 2003, 15 pages

Appeared in: Discrete and Computational Geometry, 34 (2005), no. 1, pp. 71 - 86

(22)

The E

Preprint, TU Berlin, April 2003, 21 pages

Appeared in: Discrete and Computational Geometry, 32 (2004), no. 4, pp. 601 - 621

_{t}-construction for lattices, spheres, and polytopesPreprint, TU Berlin, April 2003, 21 pages

Appeared in: Discrete and Computational Geometry, 32 (2004), no. 4, pp. 601 - 621

Proceedings

(23)

Defect Polytopes and Counter-Examples With polymake

Preprint, TU Darmstadt, May 2011, 4 pages

Appeared in: ACM Communications in Computer Algebra, 45 (2011), no. 3/4, pp. 177-179

Preprint, TU Darmstadt, May 2011, 4 pages

Appeared in: ACM Communications in Computer Algebra, 45 (2011), no. 3/4, pp. 177-179

(24)

Cyclic Permutation Polytopes

Preprint, TU Darmstadt, August 2012, 4 pages

Appeared in: DMTCS Proceedings of FPSAC 2012, AK (2012), pp. 421 - 532

Preprint, TU Darmstadt, August 2012, 4 pages

Appeared in: DMTCS Proceedings of FPSAC 2012, AK (2012), pp. 421 - 532

[journal]

(25)

Generating Smooth Lattice Polytopes

Preprint, FU Berlin, July 2010, 4 pages

Appeared in: Proceedings of the Third International Congress on Mathematical Software 2010, Lecture Notes in Computer Science, 6327 (2010), pp. 315 - 328

Preprint, FU Berlin, July 2010, 4 pages

Appeared in: Proceedings of the Third International Congress on Mathematical Software 2010, Lecture Notes in Computer Science, 6327 (2010), pp. 315 - 328

(26)

polymake and Lattice Polytopes

Preprint, FU Berlin, February 2009, 4 pages

Appeared in: DMTCS Proceedings of FPSAC 2009, AK (2009), pp. 491 - 502

Preprint, FU Berlin, February 2009, 4 pages

Appeared in: DMTCS Proceedings of FPSAC 2009, AK (2009), pp. 491 - 502

Lecture Notes

(27)

Lattices in Optimization

TU Darmstadt, August 2022, 233 pages

TU Darmstadt, August 2022, 233 pages

[pdf]

(28)

Programmieren in C

TU Darmstadt, February 2021, 302 pages

TU Darmstadt, February 2021, 302 pages

[pdf]

(29)

Algorithmic Discrete Mathematics

TU Darmstadt, August 2020, 133 pages

TU Darmstadt, August 2020, 133 pages

[pdf]

(30)

Lattice Polytopes

TU Berlin, July 2019, 101 pages

TU Berlin, July 2019, 101 pages

[pdf]

(31)

Polyhedral Geometry and Linear Optimization

FU Berlin, July 2010, 131 pages

FU Berlin, July 2010, 131 pages

[pdf]

(32)

Elementargeometrie

FU Berlin, August 2007, 79 pages

FU Berlin, August 2007, 79 pages

[pdf]

Theses