17:00
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 difference operators. In this talk, we shall discuss
series derivations and series logarithms on $\mathbb{R}((\Gamma))$ (that is, derivations that
commute with infinite sums and satisfy an infinite version of Leibniz rule, and
logarithms that commute with infinite 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.