**Raid Braid: Fast Conjugacy Class Disassembly in Groups with
Applications to the Braid Groups**

The knot classification problem is one of the most important
problems on the boundary of pure and applied mathematics. A famous theorem
of Markov showed that this can be approached via combinatorial group theory.
The Markov problem must be solved in two stages: The conjugacy problem must
be solved in each member of a family of groups and then a combinatorial
problem in their union must be solved. The question of whether the first can
be done efficiently is an important question first raised in 1969 by Garside
who presented the first solution (albeit inefficient) to this problem. Many
people have published solutions to the problem but all inefficient. This
talk will introduce the first efficient solution which puts the practical
classification of knots back on the drawing board. It will be outlined how
the method can be used for a wide class of groups and not just for the braid
groups.

*Patrick Bangert*