Orador Convidado: Claudio Piedade, CMUP, Universidade do Porto

Abstract: In 1892, Klein’s Erlangen program proposed that all geometric problems should ultimately be studied through the lens of group theory. In the 1950s, Jacques Tits introduced coset geometries, a structure that bridges geometries and their automorphism groups, allowing properties of groups to be studied via geometry and vice versa.

Coset geometries play a central role in establishing a one-to-one correspondence between regular polytopes and their automorphism groups. Consequently, classifying incidence structures becomes equivalent to classifying groups with particular properties.

This correspondence between group and geometry also makes it possible to extend classical group constructions — such as free products, HNN-extensions, and semi-direct products — into the geometric setting, where they appear as natural geometric operations.

In this seminar, we will show how one can build a coset geometry from any group, as well as how properties of the group relate with properties of the geometry.

Online: https://bigbluebutton.uevora.pt/rooms/jbv-e2n-yhk-qqj/join