#
Monday Lecture and Colloquium

**Monday, December 17, 2007 **

Technische Universität Berlin

Fakultät II, Institut für Mathematik

Str. des 17. Juni 136,

room MA 041

** Lecture - 14:15**

###
Bernd Sturmfels - TU Berlin

### Can Biology lead to New Theorems?

*Abstract:*

This lecture argues for an affirmative answer to the question in the title. In future interactions between mathematics and biology, both fields will contribute to each other, and, in particular, research in the life sciences will inspire new theorems in pure mathematics. This opinion is illustrated by four theorems on discrete structures.

**Colloquium - 16:00**

### Mareike Massow - TU Berlin

### Extremal Linear Extensions

*Abstract:*

Given a finite poset $P$, we consider pairs of linear extensions of $P$
with maximum distance. The distance of two linear extensions $L_1, L_2$
is the number of pairs of elements of $P$ appearing in different order
in $L_1$ and $L_2$. A diametral pair maximizes the distance among all
pairs of linear extensions of $P$. Diametral pairs are e.g. of interest
because their intersection forms a two-dimensional poset close to $P$.
We are interested in analyzing extremal linear extensions, i.e., those
contained in a diametral pair. I will present a conjecture and partial
results suggesting a connection between extremal linear extensions and
critical pairs of $P$. I will also present some proofs, using the
concept of the linear extension graph of $P$: Every linear extension
represents a vertex of this graph, and two of them are adjacent if they
only differ by an adjacent transposition.
This is joint work with Stefan Felsner.

Letzte Aktualisierung:
21.11.2007