Title: Interpretable groups and fields in various valued fields

Abstract: Identifying and characterizing the groups and fields one can define in various first order structures has had multiple applications within model theory and in other branches of mathematics; we review some of the results in this area.

In a recent work, we classify the interpretable fields in various valued fields, including: algebraically closed valued fields, real closed valued fields and the p-adic numbers. We show that in each of these cases, there are no surprises: they all come from either the base field or the residue field.

If time permits, we present some more recent results on interpretable groups in such valued fields and show any such group of "dimension one" is abelian-by-finite.

No knowledge in model theory will be assumed, but some basic knowledge in logic will help.

This is joint work with Assaf Hasson and Ya'acov Peterzil.


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