Lectures and Colloquia during the semester

**Monday, November 1, 2004**

Freie Universität Berlin - Institut für
Informatik

Takustraße 9

14195 Berlin

Room 005
- map -

**Lecture - 14:15**

### Jeff Erickson -University of Illinois

### Greedy optimal homotopy and homology generators

*Abstract:*
We describe simple greedy algorithms to construct the shortest set of
loops that generates either the fundamental group (with a given
basepoint) or the first homology group (over any fixed coefficient
field) of any oriented 2-manifold. In particular, we show that the
shortest set of loops that generate the fundamental group of any
oriented combinatorial 2-manifold, with any given basepoint, can be
constructed in *O(n log n)* time using a straightforward application of
Dijkstra algorithm. This solves an open problem of Colin de Verdière
and Lazarus.

This is joint work with Kim Whittlesey.

**Colloquium - 16:00**

### Ivan Izmestiev -Freie Universität Berlin

### On the hull number of torus links

*Abstract:*
The *n*-th hull of a union of curves in *R^3* is the set of points with
the property:
Any plane passing through the point intersects the curves at least *2n*
times. The hull number *u(L)* of a link *L* is defined as the minimum
number of non-empty hulls a representative of *L* can have. In the talk
we will show that the hull number of torus links (links that can be
drawn on an unknotted torus) is smaller than expected, but still
large. In particular, for a link of type *(p,p)* it is equal to *3p/5*,
and in general for the type *(p,q)* with *q>p* it is greater than or equal
to *p/2*.

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