Several problems in arithmetic geometry identify a class of "special points" and seek to describe the set of special points satisfying a given system of algebraic equations. Two classical examples are the Manin-Mumford conjecture concerning torsion points in abelian varieties, and the Andre-Oort conjecture concerning CM points in Shimura varieties. We propose a new variation on this theme, where the role of special points is played by the roots of classical orthogonal polynomials. The proof uses o-minimality in a manner analogous to the proofs of Manin-Mumford and Andre-Oort, but several features distinguish this case from the more classical arithmetic contexts. While the classical applications can be carried out in the o-minimal structures R_an or R_{an,exp}, this new variant requires the more "exotic" structure of Gevrey multisummable series; and while the classical applications involve differential Galois groups of regular-singular differential equations, this new variant leads to differential equations with irregular singularities. In the first talk, we will recall the Manin-Mumford conjecture and introduce the orthogonal polynomial analog. We will sketch the proof of Manin-Mumford using o-minimality and how it can be adapted to this new context using multisummable functions. In the second talk, we will discuss new functional transcendence results that are needed to complete the argument: a variant of the Ax-Schanuel theorem for this context. We will show how this is derived by combining recent work by Blasquez-Sans--Casale--Freitag--Nagloo with a classic paper of Kolchin. All the results are based on joint work with Avner Kiro.