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Metastability

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Metastability
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22
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CC Attribution - NonCommercial - NoDerivatives 4.0 International:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
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In their work on the model theory of algebraically closed valued fields, Haskell, Hrushovski and Macpherson developed a notion of stable domination and metastability which tries to capture the idea that in an algebraically closed valued field, numerous behaviors are (generically) controlled by the value group and/or the residue field. In this talk I will explain how (finite rank) metastability can be used to decompose commutative definable groups, in term of stable groups and value group internal groups. Time permitting, I will quickly describe the applications of these results to the study of algebraically closed valued fields, in particular, the classification of interpretable fields.