# Graduiertenkolleg: Methods for Discrete Structures

Deutsche Forschungsgemeinschaft
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# Monday Lecture and Colloquium

Monday, January 28, 2008
Technische Universität Berlin
Fakultät II, Institut für Mathematik
Str. des 17. Juni 136,
room MA 041

Lecture - 14:15

### Tilings and dissections: Three proofs

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

### Bol Loops

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.

Letzte Aktualisierung: 16.01.2008