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 and tropical geometry, mathematical software
I am currently serving as the Deputy Director of my institute
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A famous construction of Gelfand, Kapranov, and Zelevinsky associates to each finite point configuration in Rn 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.
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), See also The SymbolicData Project.
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.