This conference will focus on enumerative combinatorics and effective properties of differential and functional equations. In enumerative combinatorics one studies discrete structures usually encoded in power series called generating functions. These generating functions satisfy some equations depending on the context. These may be algebraic equations, differential equations, difference equations, Mahler equations, or more general functional equations.
Some problems require to search for the equations satisfied by such a generating function. On the other hand, once the equation satisfied by the generating equation is known, some problems require to find the nature of the series: is it an algebraic series, a D-finite series, an algebraically differential series?
The conference will explore these topics, in particular in relation with the topics of the previous week. There will be introductory courses for non-specialists.