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SUMMARY:Localization-type theorems for families of curves - Samouil Molcho
 \, Università degli Studi di Roma &quot\;La Sapienza&quot\;
DTSTART:20241024T131500Z
DTEND:20241024T141500Z
UID:TALK222163@talks.cam.ac.uk
CONTACT:Dhruv Ranganathan
DESCRIPTION:Given a smooth projective variety X with an action of a torus 
 T\, the localization theorem describes the equivariant cohomology of X ins
 ide the equivariant cohomology of the fixed point locus of the action. In 
 this talk\, I will describe how this sort of structure persists for variou
 s geometrically meaningful subrings of the cohomology (or Chow) ring of an
 y smooth S with a normal crossings divisor\, even though no group action i
 s present. I will then specialize to subrings that originate from a family
  of curves over S -- for example\, the tautological ring of the moduli spa
 ce of curves\, which originates from the universal family of the moduli sp
 ace -- and discuss how this formalism allows to calculate the classes of s
 everal loci in S\, coming from Gromov-Witten theory and Brill-Noether theo
 ry.  
LOCATION:CMS MR4
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