Self-similar groups: Automorphisms of rooted trees

This lecture by the instructor covers the topic of self-similar groups, focusing on automorphisms of regular rooted trees. The lecture starts with an introduction to the importance of studying groups acting on rooted trees. It then delves into the concept of self-similar groups and discusses the Gromov Postulate. The lecture progresses to explore residually finite groups and their properties, including the intersection of normal subgroups and the concept of finiteness. The instructor also explains the notion of pro-finite and pro-p completions of groups. The lecture concludes with a discussion on congruence subgroups and the congruence subgroup property in SL(d, Z).