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CATEGORIES:Junior Geometry Seminar
SUMMARY:Enumerative geometry and Kontsevich's formula for
counts of rational curves in a plane - Ajith Kumar
an\, University of Cambridge
DTSTART;TZID=Europe/London:20220128T160000
DTEND;TZID=Europe/London:20220128T170000
UID:TALK166663AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/166663
DESCRIPTION:Enumerative geometry is about counting subvarietie
s in an ambient variety X. We consider the concret
e question of how many rational plane curves of de
gree d pass through 3d-1 points in general positi
on. Maxim Kontsevich gave a proof of a beautiful r
ecursive formula that computes these numbers. We w
ill give a sketch of his proof using Gromov-Witten
theory. The basic idea is to turn this enumerativ
e question into a computation in the cohomology ri
ng of a certain moduli space M. This moduli space
itself may be complicated but we have natural maps
to other moduli spaces M'\, which we understand b
etter. This allows us to pullback relations in H*(
M') to H*(M). An instance of such a relation is th
e WDVV equation which will give us the aforementio
ned recursive formula.
LOCATION:MR13
CONTACT:Macarena Arenas
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