Benjamin Blanchette, here at UQAM, has just started a math blog. He will be beginning his master’s studies in september under the supervision of Christophe Reutenauer. At least until then, he’s writing about automatic groups and geometric group theory.

#### What are automatic groups?

Let be a group with a finite generating set . Any element of can be represented by a string of characters using the elements of and their inverses as letters. If the group , with this specified generating set , is *automatic,* then an automata can determine precisely when two such character strings represent the same element of .

Thus automatic groups admit a representation as character strings that is particularily easy to work with on a computer.

But I’m not an expert and there’s much more to it. Go check out bbgrouptheory.blogspot.com!