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...
AbstractIn several occasions, I have talked about some recent progresses on the unstable homotopy of manifolds made by Stephen Theriault and myself. But no details of the proof were presented. In this homotopy seminar talk, I would like to focus on one work in this project, that is, the loop homotopy decomposition of manifolds stabilized by projective spaces. We may work out some proofs togethe...