Spaces, Functions and Numbers Seminar: Bejleri -- Compact moduli and degenerations

Speaker: Dori Bejleri (University of Maryland) 

Title: Compact moduli and degenerations 

Abstract: It has been said that working with non-compact spaces is like trying to hold
change in your pocket with a hole in it.  One of the central examples of non-compact
spaces in algebraic geometry are moduli spaces.  

Broadly speaking, the points of a moduli space represent equivalence classes of
algebraic varieties of a given type, and its geometry reflects the ways these varieties
deform in algebraic families.  The classification of algebraic varieties of a given type
is tantamount to understanding the geometry of the corresponding moduli space.  

The goal of this talk is to discuss recent progress on compactifying moduli spaces of
higher dimensional varieties, focusing on the interplay between compactifications of
moduli spaces and singular degenerations of the objects they classify.  

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