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SUMMARY:Logarithmic and orbifold Gromov-Witten invariants
DTSTART:20220322T101500
DTEND:20220322T120000
DTSTAMP:20260528T083121Z
UID:bf40a89a36f851cac34bc4123399e2d0521831b62695599c84eb0327
CATEGORIES:Conferences - Seminars
DESCRIPTION:Luca Battistella (University of Heidelberg)\nLogarithmic Gromo
 v-Witten theory can be thought of as the study of curves in open manifolds
 \, or\, in other words\, curves with tangency conditions to a boundary div
 isor. When the divisor is smooth\, several techniques have been deployed t
 o compute the invariants\, most notably twisted stable maps\, and recursiv
 e schemes based on the degeneration formula. When the divisor is normal cr
 ossings\, on the other hand\, the logarithmic theory remains hardly access
 ible (with some exceptions in the surface or toric case). The strategy of 
 rank reduction\, i.e. looking at the components of the boundary one at a t
 ime\, is more directly applicable to other theories than the logarithmic o
 ne (as shown in Nabijou-Ranganathan\, and B.-Nabijou-Tseng-You) because of
  tropical obstructions. Inspired by one of the distinguishing features of 
 the logarithmic theory - being insensitive to modifications of the boundar
 y [Abramovich-Wise] - and further building on the work of Abramovich-Cadma
 n-Marcus-Wise and Tseng-You\, in an ongoing project with Nabijou and Ranga
 nathan we show that genus zero tropical obstructions can be disposed of by
  blowing up the target sufficiently. The slogan is that the orbifold and l
 ogarithmic theories can be made to agree by imposing birational invariance
  on the former.
LOCATION:MA A1 10 https://plan.epfl.ch/?room==MA%20A1%2010
STATUS:CONFIRMED
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