Monday, May 30, 2016
Freie Universität Berlin
Takustr. 9
14195 Berlin
room 005
Lecture - 14:15
Abstract:
Gil Kalai has written that "It is not unusual that a single example or a very few shape an entire mathematical discipline. Examples are the Petersen graph, cyclic polytopes, the Fano plane, the prisoner dilemma, the real n-dimensional projective space and the group of two by two nonsingular matrices. And it seems that overall, we are short of examples. The methods for coming up with useful examples in mathematics (or counterexamples for commonly believed conjectures) are even less clear than the methods for proving mathematical statements."
In this lecture, I will take this as an excuse to describe my own "top 10 list" of polytopes. (You might draw up your own, of polytopes, of graphs, of designs, etc.) For each of them, I will want to sketch what I/we know about them, why they are interesting/remarkable, and what open questions and mysteries remain.
Colloquium - 16:00
Abstract:
A space group is a discrete group of isometries with bounded
fundamental domain. Prominent examples are the 17 wallpaper groups and
219 crystallographic groups. Bieberbach proved that in each dimension
there are only finitely many non-isomorphic space groups, and much later
Buser gave the first upper bound. We will show how to improve Buser's
bound considerably and get close to known lower bounds. As an
application of our result we bound the number of conjugacy classes of
finite subgroups of GL(n,Z).