Prof. Dr. Michael Joswig

Einstein Professor of Discrete Mathematics/Geometry
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
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.



Teaching and Seminars

Winter 2015/16
On sabbatical leave.

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.

Polyhedral fan structures in toric and tropical geometry

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.


See also The SymbolicData Project.

Multiview geometry for ophthalmic surgery simulation

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.

Mathematical Software

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.



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.


Oberwolfach References on Mathematical Software

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.

Upcoming Events


Editorial Work

Member of ...

Berlin Mathematical School

Research Training Group "Methods for discrete structures"

Research Center Matheon

TRR 109 "Discretization"

Deutsche Mathematiker-Vereinigung

Research funded by ...

Previous Projects

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Last modified: Mon May 13:20:43 UTC 2016 by joswig