AbstractThe goal of this minicourse is to introduce the recent advances in Hodge theory via o-minimal techniques. We will start by revisiting the basics on o-minimal geometry with a view towards algebraization theorems (Pila-Wilkie counting theorem; o-minimal Chow and GAGA theorems in definable complex analytic geometry). In the realm of Hodge theory, we will explore several applications: (i) t...
AbstractThe Langlands program posits that automorphic forms associated to a reductive group are parametrized by Galois representations valued in its dual group. Around ten years ago, Weissman-Gan-Gao proposed an extension of the Langlands program which puts covering groups (such as the metaplectic group) under the same framework. In this minicourse, I will explain how to systematically study su...