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|
|Email:||lastname at math.tu-berlin.de|
Office hours: by appointment
Research areas: polyhedral geometry, mathematical software
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.
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.
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.
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.