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Abstract:
In this talk we will discuss some recent joint works with Liu,
Yau and with Todorov about the geometry of moduli spaces of algebraic
curves and polarized Calabi-Yau manifolds. We will discuss new metrics on
the curve moduli, their curvature and asymptotic properties. We will also
discuss the consequences in algebraic geometry such as the stability of
log tangent bundles of the Deligne-Mumford moduli spaces, Chern number
inequality, Gauss-Bonnet theorem and good geometry. We will also discuss
the flat coordinate construction and properties of period maps of the
Teichmuller space of polarized CY manifolds.
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