Geometry of A_g and its compactifications -- Samuel Grushevsky

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We will survey the progress made in the last decade in understanding the
geometry of the moduli spaces of polarized abelian varieties and their
various compactifications.

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Among other topics, we will discuss moduli problem interpretations, the
ample and effective cones, canonical models for A_g, Chow groups, homology
and intersection theory, subvarieties of the moduli spaces, and the geometry
of the theta divisor.