Valued di fferential fields of exponential logarithmic series.

Valued di fferential fields of exponential logarithmic series.

Thu, 02/12/2010
17:00 		Salma Kuhlmann (Konstanz) Logic Seminar Add to calendar L3
Valued di fferential fields of exponential logarithmic series.
Consider the valued field $ \mathbb{R}((\Gamma)) $ of generalised series, with real coefficients and monomials in a totally ordered multiplicative group $ \Gamma $ . In a series of papers, we investigated how to endow this formal algebraic object with the analogous of classical analytic structures, such as exponential and logarithmic maps, derivation, integration and di fference operators. In this talk, we shall discuss series derivations and series logarithms on $ \mathbb{R}((\Gamma)) $ (that is, derivations that commute with in finite sums and satisfy an in finite version of Leibniz rule, and logarithms that commute with infi nite products of monomials), and investigate compatibility conditions between the logarithm and the derivation, i.e. when the logarithmic derivative is the derivative of the logarithm.