Achill Schürmann

Achill's Research Interests

outdated since August 2009
new page at University of Rostock

I am interested in any nice problem, but my current research interests may be subsumed to lie in computational mathematics. Problems I have worked on fall into the following more specific categories:

Discrete and Algorithmic Geometry
Geometry of Numbers, Packing- and Covering problems
Quadratic Forms, Reduction theories
Combinatorial Geometry, Polyhedral Combinatorics
Convex Geometry, Minkowski Spaces
Optimization, Linear and Convex Programming techniques
Codes and Designs
Algorithms and Complexity theory

Since May 2005 my research on the Geometry of Lattices, together with Frank Vallentin, is supported by the Deutsche Forschungsgemeinschaft (DFG) under grant SCHU 1503/4.

I like computers and think it is not only fun, but also very helpful to use mathematical software to explore math. Sometimes we have to develop suitable programs ourselves (see for example rmd, coop, pacoop, scc which are joint projects with Frank Vallentin).

Some of my work on the geometry of lattices (or positive definite quadratic forms if you prefer) is described in my book on "Computational Geometry of Positive Definite Quadratic Forms".

I have (co)organized the following events:

Minisymposium Discrete Geometry and Topology at the DMV meeting 2008 in Erlangen, September 2008.
Workshop on Experimentation with, construction of, and enumeration of optimal geometric structures , Bonn, March 2008.
Workshop Linear and semidefinite programming bounds , Bonn, February 2008.
Trimester Program on Extreme Geometric Structures at the Hausdorff Research Institute for Mathematics in Bonn, February to April 2008.
Oberwolfach Seminar on Sphere Packings: Exceptional Geometric Structures and Connections to other Fields , Oberwolfach, November 2005.

Once a week I participate in our special research group (Mathe-Kick) on the world's most popular dynamical system... :-)