Two groups are considered ‘elementarily equivalent’, if they have the same ‘elementary’ theory. Classification of various families of groups based on elementary equivalence, has been of long standing interest to both group theorists and model theorists, the most celebrated example of which was the elementary equivalence in free groups posed by Tarski. By studying examples of groups with different elementary theories, we can gain insight into the nature of expressibility of properties of groups. In this talk, I shall elementary equivalence in Artin groups of finite type, which forms a generalization of braid groups and are of interest in geometric group theory. This was a part of joint work with Arpan Kabiraj and Rishi Vyas. The talk should be largely self-contained. No background in logic, model theory or braid groups shall be assumed.

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Last updated: 17 Oct 2019