Abstract:The tropical methods have already been used to study the moduli theory of algebraic curves during the past decade. In this talk, I will first discuss about the tropicalization of a smooth pointed Riemann surface via its (hyperbolic) pair of pants decomposition, and then about how to compactify the moduli space of tropicalizations in a geometrically meaningful way
AbstractThe non-abelian Hodge theory identifies moduli spaces of representations with moduli spaces of Higgs bundles through solutions to Hitchin's selfduality equations. On the one hand, this enables one to relate geometric structures on surfaces with algebraic geometry, and on the other hand, one obtains interesting hyper-Kähler metrics on the solution spaces. In my talk, I will explain how t...