Monday, January 28, 2008
Technische Universität Berlin
Fakultät II, Institut für Mathematik
Str. des 17. Juni 136,
room MA 041
Lecture - 14:15
Abstract:
My plan is to present three results about
tilings and dissections with proofs "of BOOK quality":
de Bruijn's theorem about tilings a rectangle
with rectangles that have an integer side;
Benko's 2007 new solution to Hilbert's Third Problem;
and Monsky's proof that no rectangle can be cut into
an odd number of equal-area triangles.
If time permits, there will be a number-theoretic encore
by Don Zagier.
Colloquium - 16:00
Abstract:
Every Latin Square whose entries are the numbers in $[n]= \{1, \ldots ,
n\}$ can be thought of as the table of a binary operation $\circ$ on
$[n]$. If it contains a neutral element, then $([n], \circ)$ is a {\em
loop}. Loops appear naturally in physics, computer science, geometry and
group theory. Those which satisfy a weak
associativity, so called {\em Bol} loops, are of special interest.
In the talk I will motivate the major longstanding open questions on Bol
loops as well as their answers,
which is joint work with Alexander Stein. Finally I will give an
application to graphs.