Seminario Nacional de Geometría Algebraica
Sung Gi Park, Princeton University.
The moduli space of smooth hypersurfaces in projective space can be constructed as a GIT quotient by linear changes of coordinates, and it comes with a natural GIT compactification. In certain degrees and dimensions, Hodge theory provides a second compactification via the period map, namely the Baily-Borel compactification.Building on recent progress on higher singularities and a new stability criterion formulated in terms of the minimal exponent (a refinement of the log canonical threshold), I will discuss the birational geometry of these two compactifications and describe consequences for the boundary behavior of the period map. 
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