AbstractThe homotopy type conjecture (weak form of geometric P=W conjecture) states that: for any (smooth) Betti moduli space $\mathcal{M}_B$ of complex dimension d over a (punctured) Riemann surface, the dual boundary complex $\mathbb{D}\partial\mathcal{M}_B$ is homotopy equivalent to a sphere of dimension d-1. The main goal of this lecture series is to explain a proof of the conjecture for an...
