Patrick Dehornoy
Alternating normal form of braids and applications

We describe new types of normal forms for braid monoids, Artin-Tits monoids,
and, more generally, all monoids in which divisibility has some convenient
lattice properties (`locally Garside monoids''). We show that, in the case
of braids, one of these normal forms turns out to coincides with the normal
form introduced by Burckel. This approach leads to a new, simple description
for the canonical well-order of B_n in terms of that of B_{n-1}. In a joint
work with A.Bovykin, L.Carlucci and A.Weiermann, we apply the latter to
establish unprovability statements for certain games involving braids.