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SUMMARY:Counting planar curves using tropical geometry - Sae Koyama\, Univ
 ersity of Cambridge
DTSTART:20250509T150000Z
DTEND:20250509T160000Z
UID:TALK229786@talks.cam.ac.uk
CONTACT:Adrian Dawid
DESCRIPTION:Tropical curves are balanced piecewise linear functions from g
 raphs into R^n\, with d “infinite legs” going in directions e_1\, e_2\
 , and -e_1-e_2. The number d is the degree of the tropical curve\, while t
 he first Betti number of the graph is the genus. We can ask enumerative qu
 estions: how many tropical curves of genus g and degree d pass through 3d+
 g-1 points? \n\nIt turns out that\, in the case of genus 0\, this number i
 s precisely the same as the number of algebraic curves of degree d and gen
 us g passing through 3d-1 points. This so-called Mikhalkin’s tropical co
 rrespondence has far-reaching consequences. If we want to count algebraic 
 curves\, we “simply” have to count tropical curves. I will introduce t
 he notion of tropicalization\, sketch the correspondence theorem\, and sug
 gest how these results may be generalised.
LOCATION:MR13
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