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...
AbstractThe geometric P=W conjecture is a conjectural description of the asymptotic behaviour of acelebrated correspondence in non-abelian Hodge theory. in a joint work with Enrica Mazzon andMatthew Stevenson, we establish the full geometric conjecture for compact Riemann surfaces ofgenus one, and obtain partial results in arbitrary genus: this is the first non-trivial evidence of theconiecture...
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