Title: Domination in Some Valued Fields and Its Applications
Abstract: The theory of algebraically closed valued fields (ACVF) is not stable. However, the stable part has a decisive role in the rest of the structure, this phenomenon is called stable domination. E. Hrushovski and S.Rideau-Kikuchi showed that it enables techniques used in stable theories and they used them to analyze definable groups and fields in ACVF. Later, Ealy, Haskell and Marikova introduced residue field domination for real closed valued fields, which is a generalization of the stable domination in ACVF. In this talk, we will go over these results and introduce and discuss our current research regarding definable groups in real closed valued fields.