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SUMMARY:Enumerative geometry and Kontsevich's formula for counts of ration
 al curves in a plane - Ajith Kumaran\, University of Cambridge 
DTSTART:20220128T160000Z
DTEND:20220128T170000Z
UID:TALK166663@talks.cam.ac.uk
CONTACT:Macarena Arenas
DESCRIPTION:Enumerative geometry is about counting subvarieties in an ambi
 ent variety X. We consider the concrete question of how many rational plan
 e curves of degree d  pass through 3d-1 points in general position. Maxim 
 Kontsevich gave a proof of a beautiful recursive formula that computes the
 se numbers. We will give a sketch of his proof using Gromov-Witten theory.
  The basic idea is to turn this enumerative question into a computation in
  the cohomology ring of a certain moduli space M. This moduli space itself
  may be complicated but we have natural maps to other moduli spaces M'\, w
 hich we understand better. This allows us to pullback relations in H*(M') 
 to H*(M). An instance of such a relation is the WDVV equation which will g
 ive us the aforementioned recursive formula. 
LOCATION:MR13
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