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Lectures and Colloquia during the semester



January 13, 2003

Technische Universität Berlin
Straße des 17. Juni 136
10623 Berlin
Math building - Room MA 042           - map -
Lecture - 14:15

Michael Joswig-Technische Universit&aum;t Berlin

Remarks on computer based mathematics

Abstract: Recent years saw a tremendous increase of computer based mathematics in a wide range of fields. This naturally raises the question of reliability of such results. Rather than discussing the logical (and philosophical) aspects, we indicate partial solutions on a more practical level. In particular, we explain how projects like polymake and Electronic Geometry Models may help.

Disclaimer: No technical details concerning programming or so are presented. Instead the talk follows a series of typical algorithmic problems arising in discrete geometry and combinatorial topology.

polymake is joint work with Ewgenij Gawrilow (TU Berlin). EG-Models is a joint project with Konrad Polthier (TU Berlin).


Colloquium - 16:00

Andreas Paffenholz-Technische Universität Berlin

Some New Constructions for Polytopes

Abstract: D. Eppstein, G. Kuperberg and G. M. Ziegler recently presented a method for the construction of 2-simplicial, 2-simple 4-polytopes (the "E-construction"). Their method can be applied to all ridge-tangent simple polytopes. This is unfortunately a severe restriction on a four dimensional polytope.

Families of such 2-simplicial, 2-simple polytopes are interesting for the problem of classifying possible flag vectors of 4-polytopes. In particular such polytopes could maximize the fatness parameter of 4-polytopes.

In my talk I will present a generalization of the construction that drops the edge-tangency requirement and gives new infinite families of rational 2-simplicial, 2-simple polytopes with many degrees of freedom. I will show that this construction can also be generalized to higher dimensions to produce some examples of 2-simple and (d-2)-simplicial d-polytopes.


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