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.

Preprints
(1)
Existence of regular unimodular triangulations --- Positive Results (joint with Christian Haase, Lindsay Piechnik, Francisco Santos)
Preprint, FU Berlin, May 2014, 82 pages
to appear in: Memoirs of the AMS
(2)
Permutation Polytopes of Cyclic Groups (joint with Barbara Baumeister, Christian Haase, Benjamin Nill)
Preprint, TU Darmstadt, September 2011, 15 pages
Publications
(3)
Smooth Polytopes with negative Ehrhart Coefficients (joint with Federico Castillo, Fu Liu, Benjamin Nill)
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
(5)
Toric Geometry in Polymake (joint with Lars Kastner, Benjamin Lorenz, Anna-Lena Winz)
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 (joint with Benjamin Assarf, Ewgenij Gawrilow, Katrin Herr, Michael Joswig, Benjamin Lorenz, Thomas Rehn)
Preprint, TU Darmstadt, August 2014, 31 pages
Appeared in: Mathematical Programming Computation, 9 (2017), no. 1, pp. 1 - 38
(7)
Finiteness of the polyhedral Q-codegree spectrum
Preprint, TU Darmstadt, January 2013, 9 pages
Appeared in: Proc. AMS, 143 (2015), no. 11, pp. 4863--4873
(8)
Finitely many smooth d-polytopes with n lattice points (joint with Tristram Bogart, Christian Haase, Milena Hering, Benjamin Lorenz, Benjamin Nill, Günter Rote, Francisco Santos, Hal Schenck)
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
(10)
Smooth Fano Polytopes with Many Vertices (joint with Benjamin Assarf, Michael Joswig)
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 (joint with Benjamin Nill)
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 (joint with Barbara Baumeister, Christian Haase, Benjamin Nill)
Preprint, TU Darmstadt, August 2011, 9 pages
Appeared in: Ars Mathematica Contemporanea, 7 (2014), no. 1, pp. 30 - 38
(13)
Polyhedral Adjunction Theory (joint with Sandra Di Rocco, Christian Haase, Benjamin Nill)
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 (joint with Benjamin Nill)
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 (joint with Christian Haase, Benjamin Nill, Francisco Santos)
Preprint, FU Berlin, September 2007, 9 pages
Appeared in: Electronic Journal of Combinatorics, 15 (2008), no. N11, pp. #N11
(16)
On Fanos and Chimneys (joint with Christian Haase)
Preprint, FU Berlin, September 2007, 3 pages
Appeared in: Oberwolfach Reports, Report 39/2007 (2007), pp. 2303 - 2306
(17)
On Permutation Polytopes (joint with Barbara Baumeister, Christian Haase, Benjamin Nill)
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 (joint with Christian Haase)
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 (joint with Axel Werner)
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
(21)
Bier spheres and posets (joint with Anders Björner, Jonas Sjöstrand, Günter M. Ziegler)
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 (joint with Günter M. Ziegler)
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 (joint with Michael Joswig)
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 (joint with Barbara Baumeister, Benjamin Nill, Christian Haase)
Preprint, TU Darmstadt, August 2012, 4 pages
Appeared in: DMTCS Proceedings of FPSAC 2012, AK (2012), pp. 421 - 532
(25)
Generating Smooth Lattice Polytopes (joint with Christian Haase, Benjamin Lorenz)
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 (joint with Michael Joswig, Benjamin Lorenz)
Preprint, FU Berlin, February 2009, 4 pages
Appeared in: DMTCS Proceedings of FPSAC 2009, AK (2009), pp. 491 - 502
Lecture Notes
(27)
Programmieren in C
TU Darmstadt, February 2021, 302 pages
[pdf]
(28)
Algorithmic Discrete Mathematics
TU Darmstadt, August 2020, 133 pages
[pdf]
(29)
Lattice Polytopes (joint with Christian Haase, Benjamin Nill)
TU Berlin, July 2019, 101 pages
[pdf]
(30)
Polyhedral Geometry and Linear Optimization
FU Berlin, July 2010, 131 pages
[pdf]
(31)
Elementargeometrie
FU Berlin, August 2007, 79 pages
[pdf]
Theses
(32)
Constructions for Posets, Lattices, and Polytopes
TU Berlin, May 2005, 208 pages
[pdf, edoc]
(33)
Geodätische Flüsse und Starrheit auf Flächen
Universität Bonn, September 2001, 132 pages
[pdf]
(34)
The Selberg Trace Formula and Determinants of the Laplacian
University of Cambridge (GB), June 1999, 80 pages
[pdf]