Title: The inverse Galois problem for some Lie type groups

Abstract: In the last years, the study of the images of the Galois representations associated to regular algebraic cuspidal automorphic representations of $GL_n(\mathbb{A}_{\mathbb{Q}})$, has been an effective strategy to address the inverse Galois problem for finite groups of Lie type. In this talk we will explain how, by combining this strategy with Langlands functoriality and globalization of supercuspidal representations, we can construct residual Galois representations with controlled image and obtain new families of finite groups of Lie type $B_m$, $C_m$ and $D_m$ arising as Galois groups over $\mathbb{Q}$.