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 Et-construction for lattices, spheres, and polytopes
Preprint, TU Berlin, April 2003, 21 pages
Appeared in: Discrete and Computational Geometry, 32 (2004), no. 4, pp. 601 - 621
Preprint, 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