Abstract: This talk presents results analogous to the classical Manin-Mumford conjecture concerning roots of Laguerre polynomials. We consider "Laguerre special points" (roots of P_k(x)) and "Laguerre special subvarieties" in (C*)^n (defined by equations x_i=x_j or x_k=p, where p is a special point). Our main results state that an algebraic subvariety V ⊂ (C*)^n containing a Zariski-dense set of Laguerre special points must be a Laguerre special subvariety. The proof employs the Pila-Zannier strategy, combining o-minimal point counting (using Gevrey asymptotics and steepest descent for definability) with an Ax-Schanuel theorem tailored for the Laguerre differential equation.