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 and tropical geometry, mathematical software

I am currently serving as the Deputy Director of my institute

- Check out our polytope game MatchTheNet!
- polymake 3.0 was released on January 18, 2016.
- The recent beta of version 3.1 supports the new polymake data base .
- 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 MathSciNet
- 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

- Baer-Kolloquium, TU Berlin, 21 January 2017

- Computer-oriented Mathematics II, VL 4+2
- Seminar, SE 2

- Computer-oriented Mathematics I, VL 4+2
- Discrete Geometry III: Tropical Combinatorics, VL+UE 4+0 + SE 2

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

A famous construction of Gelfand, Kapranov, and Zelevinsky associates to each finite point configuration in **R**^{n} its secondary fan, which stratifies the space of height functions by the combinatorial types of coherent subdivisions. A completely analogous construction associates to each punctured Riemann surface a polyhedral fan, whose cones correspond to the ideal tessellations of the surface that occur as horocyclic Delaunay tessellations in the sense of Penner's convex hull construction. We suggest to call this fan the secondary fan of the punctured Riemann surface. The purpose of this project is to study these secondary fans of Riemann surfaces and explore how their geometric and combinatorial structure can be used to answer questions about Riemann surfaces, algebraic curves, and moduli spaces.

Project A11 in the SFB/TRR 109, with Boris Springborn. Researcher: Robert Loewe.

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),

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
- Polytropes in the tropical projective 3-torus

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,
*Int. J. Algebra Comput.***26**(2016) (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 3.0r2 (from Jan 2016, with added support of recent compilers and Perl versions) 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.

- Baer-Kolloquium, TU Berlin, 21 January 2017
- MSRI Program: Geometric and Topological Combinatorics, Berkeley, Aug-Dec 2017
- IML Program: Tropical Geometry, Amoebas and Polytopes, Stockholm, Jan-Apr 2018
- ICMS 2018: 6th International Congress of Mathematical Software, Notre Dame, 24-27 July 2018

- Tropical Combinatorics, Hausdorff School: Economics and Tropical Geometry, Bonn 9-13 May 2016. [polymake code]
- Meeting Einstein public lecture: "Museums, triangles and algebraic curves", 28 May 2015.

- Bernd Sturmfels (UC Berkeley and TU Berlin), Einstein Visiting Fellow, 2015-2018
- Antoine Deza (McMaster), January 2017
- Stephan Tillmann (U Sydney), 2017