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SUMMARY:N. Takahashi's 3 Conjectures - Michel van Garrel (University of Bi
 rmingham)
DTSTART:20220722T133000Z
DTEND:20220722T143000Z
UID:TALK176678@talks.cam.ac.uk
DESCRIPTION:Consider the log K3 surface given by the pair of the projectiv
 e plane and an elliptic curve. Based on rather intricate computations\, N.
  Takahashi stated 3 influencial conjectures in 2001. They are (1) the log-
 local correspondence\, (2) the BPS log-local correspondence and (3) the B-
 model to the log K3 surface. While (1) was proven for the plane shortly af
 terwards by Gathmann\, a proof in all generality only came in 2017 with su
 bsequent ongoing variations on the theme.\nThe proof of (2) was completed 
 in 2019 through a sequence of works by Gr&auml\;fnitz and Bousseau that ne
 cessitated the study of wall-crossing in spaces of Bridgeland stability co
 nditions\, a non-existent notion in 2001. Generalisations to other log K3 
 surfaces are currently out of reach.\nMy talk will be about (3)\, which we
  prove in joint work with Ruddat and Siebert. By using the mirror construc
 tion of the Gross-Siebert programme\, we obtain exactly the prediction by 
 Takahashi from more than 20 years ago.
LOCATION:Seminar Room 1\, Newton Institute
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