Title:

Infinitesimal groups in valued fields and some applications

Abstract:I will review some recent results on interpretable groups and fieldsin various valued fields.In the proof of these results certain infinitesimal groups play acrucial role and  "locally connect" the interpretable group to one ofthe following sorts: K (the valued field), \Gamma (the value group), k(the residue field) or K/O (the collection of closed 0-balls). Thisallows to pass algebraic properties from these sorts to thegroup\field.All notions will be explained.

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