Abstract. In this expository talk we will present the main obstructions to establish a useful summability method able to treat formal power series solutions in several variables, of analytic problems such as singularly perturbed ODEs and PDEs with holomorphic coefficients.
We will discuss first the situation in the case of one variable. We exemplify how $k-$summability in the sense of Borel is useful in generic situations but multisummability is necessary to treat the above problems. Then for higher dimensions we explain some available approaches, including the recent work on $k-$summability in an analytic germ.
Please click here for the slides of the talk.