Institut für Mathematik der Technischen Universität Berlin Sekretariat MA 6-2 Straße des 17. Juni 136 10623 Berlin, Germany |

Phone: | +49 (30) 314 - 75904 |

Office: | +49 (30) 314 - 28643 |

Fax: | +49 (30) 314 - 25047 |

Room: | MA 623 |

Email: | lastname at math.tu-berlin.de |

OpenPGP: | public key |

Office hours: by appointment

Research areas: polyhedral geometry, mathematical software

- polymake 3.0 was released on January 18, 2016. Packaged versions available for most Linux distros and MacOS X. Ubuntu 16.04 (xenial) coming up.
- DGD Gallery
- I am (still) working on a forthcoming book "Essentials of Tropical Combinatorics". Take a look at the web page with a working draft and send comments.

- complete list of publications
- according to Mathematical Reviews
- according to Zentralblatt MATH
- arXiv preprints

- (with Thorsten Theobald): Polyhedral and Algebraic Methods in Computational Geometry, Springer 2013, translated and revised from Algorithmische Geometrie [German], Vieweg 2008.
- (with Komei Fukuda, Joris van der Hoeven, and Nobuki Takayama, eds.): Mathematical Software - ICMS 2010, Proceedings, LNCS 6327, Springer 2010
- (with Nobuki Takayama, eds.): Algebra, Geometry, and Software Systems, Springer 2003

- Discrete Geometry II, VL 4+2
- Topics in Gröbner Bases, SE 2

Students interested in the seminar on Gröbner bases are required to attend the meeting on Wednesday, April 20, at **14:00** (time changed!) in MA621.

Click on an icon for more detailed information about a project.

A polyhedral fan is formed of polyhedral cones which meet face to face. Prominent examples include the normal fan of a polytope (which encodes everything there is to say about that polytope from a linear optimization point of view), the secondary fan of a point configuration (which stratifies the regular subdivisions of the convex hull, using the given points), and the Gröbner fan of an ideal in a polynomial ring (which describes all possible Gröbner bases for that idea. The key objects in tropical and toric geometry belong here as well. Projective toric varieties can be described in terms of the normal fans (or dually, the face fans) of lattice polytopes. Tropical varieties occur as subfans of Gröbner fans.

Project in the DFG Priority Program SPP 1489. Researcher: Simon Hampe.

- Predecessor project: Decompositions of lattice polytopes
- Tight spans of finite metric spaces
- Defect polytopes and counter-examples with polymake

See also The SymbolicData Project.

A fundamental problem in machine vision asks to generate geometric information about a scene in 3-space from several camera images. This is relevant, e.g., in the context of augmented reality frameworks for eye surgery simulation. It is the goal of this project to apply techniques from geometric combinatorics and algebraic geometry for analyzing the picture space to allow for a profound computational preprocessing.

Project CH03 in the Einstein Center for Mathematics Berlin. Researcher: André Wagner.

- Rigid Multiview Varieties, arXiv:1509.03257 (with Joe Kileel, Bernd Sturmfels and André Wagner) [Macaulay2 code]
- Conference: Algebraic Vision, TU Berlin, 8-9 Oct 2015.

Specialized software is the key tool to help the mind doing research in mathematics. At the same time mathematical software bridges the gap between the diverse fields of mathematics and their application areas.

polymake is a software system for convex polytopes, simplicial complexes, and more. Co-authored with Ewgenij Gawrilow (now TomTom) and actively supported by many people [BibTeX-Entry]. If you are interested to see how polymake can be used, see the documentation or this extra page with references.

- Get an idea of how to use the system from the polymake Miscellanea.
- Look up polymake at swMATH.
- The polymake release 3.0r1 (from Jan 2016) is available as a Debian package. It also comes, e.g., with Ubuntu 16.04 (Xenial Xerus).

A new collection of geometric models.

This is a small program which computes real representations of quasi-simple Lie groups. It is quite old but still functional and occasionally useful. Joint work with Richard Bödi.

The ORMS is a web-interfaced collection of information and links on mathematical software. It presents carefully selected software, including general purpose software systems, teaching software, and more specialized packages up to specific implementations on particular mathematical research problems. See also swMATH.

- Homological and Computational Methods in Commutative Algebra, Cortona, 29 May - 4 June 2016
- Workshop on Discrete and Non-Linear Geometry (co-organized with Bernd Sturmfels), TU Berlin, 16-17 June 2016
- A New Era of Discrete and Computational Geometry, Ascona, 26 June - 1 July 2016
- ICMS 2016 : 5th International Congress of Mathematical Software, ZIB, Berlin, 11-14 July 2016. Session "Polyhedral methods in geometry and optimization" (co-organized with Marc Pfetsch).
- 7th European Congress of Mathematics, TU Berlin, 18-22 July 2016
- Algebraic Statistics and Symbolic Computation, RIMS Kyoto, 25-29 July 2016
- Workshop on Convex Polytopes, RIMS Kyoto, 1-5 Aug 2016
- Dagstuhl Seminar "Algorithms and Effectivity in Tropical Mathematics and Beyond" (12-0116), 27 Nov - 2 Dec 2016 (co-organized with Stéphane Gaubert, Dima Grigoriev and Thorsten Theobald)
- Baer-Kolloquium, TU Berlin, 21 January 2017

- Tropical Combinatorics, Hausdorff School: Economics and Tropical Geometry, Bonn 9-13 May 2016. [polymake code]
- "polymake: Software for Polytope Constructions in Linear and Integer Optimization", Combinatorial Optimization at Work, ZIB Berlin, 29 Sep 2015. [Teaching Material]
- Meeting Einstein public lecture: "Museums, triangles and algebraic curves", 28 May 2015.

- Bernd Sturmfels (UC Berkeley and TU Berlin), Einstein Visiting Fellow, 2015-2017
- Amanda R. Cameron (Queen Mary University of London), 2016
- Jules Depersin (École Polytechnique), 2016
- Stephan Tillmann (U Sydney), 2016
- Guillermo Pineda-Villavicencio (Federation University Australia), 2016