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UID:c3967bfc833bf4c2c840446155afb8cf
CATEGORIES:Colloquia
CREATED:20251017T132051
SUMMARY:Compactifying Moduli of Algebraic Varieties
LOCATION:Hill 705
DESCRIPTION:<p>Hodge Theory provides a general way of understanding moduli spaces of al
 gebraic varieties: Given a family of algebraic varieties, one obtains a `pe
 riod map' by considering the hodge structure on the cohomology. However, th
 ese period maps are built from period integrals, and are highly transcenden
 tal, which&nbsp;yields challenges when one wants to recover an algebraic st
 ructure.&nbsp;</p><p>Famously, this story works really nicely for the modul
 i space of (principally polarized, g-dimensional) Abelian varieties A_g, wh
 ere the hodge theory gives an exact&nbsp;moduli space, and the work of Bail
 y-Borel provides a beautiful compactification of this space which can also 
 be understood using hodge theory.&nbsp;</p><p>We explain how this picture g
 eneralizes to arbitrary period maps. This has especially nice applications 
 to moduli spaces of Calabi-Yaus, which has proven less accessible to other&
 nbsp;techniques. Moreover, the same tools yield a resolution of the&nbsp; b
 -semiampleness conjecture of Prokhorov and Shokurov. This is joint work wit
 h Bakker, Filipazzi, and Mauri.</p>
CONTACT:Jacob Tsimerman
DTSTAMP:20260829T200337
DTSTART;TZID=America/New_York:20251024T153000
DTEND;TZID=America/New_York:20251024T163000
SEQUENCE:0
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