Time: 2019-05-31 15：30-17：30

Venue: Room 201 Lecture Hall

Abstract:

The set of idempotents of any semigroup carries the structure of a biordered set, which contains a great deal of information concerning the idempotent generated subsemigroup of the semigroup in question. This leads to the construction of a free idempotent generated semigroup $IG(E)$ šC the `free-est' semigroup with a given biordered set $E$ of idempotents. It was thought from the 1970s that all maximal subgroups of $IG(E)$ would be free, but this conjecture was false. In this talk, I will present my recent 5 years research progress joint with my collaborators on this topic, including maximal subgroups, general structures and word problems of $IG(E)$.