Abstract
Recall that an Artin group is called of spherical type if its associated Coxeter group is finite. It is known that the irreducible spherical Artin groups consist of four infinite families, the groups of type An𝐴𝑛, the groups of type Bn𝐵𝑛, the groups of type Dn𝐷𝑛 and the groups of type I2(m)𝐼2(𝑚), and 66 sporadic groups. The groups of type An𝐴𝑛 are the braid groups and they can be easily understood using various algebraic and/or topological methods. The groups of type Bn𝐵𝑛 are finite index subgroups of the groups of type An𝐴𝑛, hence the methods used to understand the groups of type An𝐴𝑛 often apply in this case as well. The groups of type I2(m)𝐼2(𝑚) are virtually direct products of a free group with Z𝑍. However, in order to understand the groups of type Dn𝐷𝑛, it is often necessary to develop new tools and they are more difficult to study. This talk will recount the different studies on these groups to culminate in the latest one, in collaboration with Fabrice Castel, where we classify the endomorphisms of such groups for a large n𝑛.