Title: O-minimality of the algebra of multisummable functions and almost regular germs.
Abstract: One approach to proving Dulac’s problem is to show that the algebra of all correspondence maps is o-minimal. Each correspondence map can be expressed as a composition of holomorphic functions, multisummable functions, and almost regular germs. In this talk, I will focus on almost regular germs, whose asymptotic expansions are generalized power series, and discuss results concerning the algebra generated by such functions. Specifically, I will explain how Patrick and I established quasianalyticity and key closure properties of this algebra, which are essential in proving o-minimality.
