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physicists calculate (predict) genus one GW invariants of quintic (Table 1) and some other cases (Table 2).

Can any body explain to me (mathematically) how do they do that? What is the B-model object (integral) which they consider and extract these numbers from (conjecturally via some mirror relation) ?

Please at least try to explain mathematically.

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Hi @MohammadF.Tehrani, I am not sure if you are still interested in this question, but it has just obtained an answer here on PhysicsOverflow. Maybe the answerer would be willing to repost it here, if you would like to have it here on MO too. – Dilaton Jul 28 '14 at 19:30
Thanks for sharing, I appreciate it. People can go through the link and study his answer. I found his answer somewhat problematic, I may suggest some reviews to him later. There is also some recent talk by Aleksey Zinger in Simons center which is related to the subject, I would share the link some time later. – Mohammad F. Tehrani Jul 30 '14 at 13:47
Dear @MohammadF.Tehrani, if you would like to discuss this with the answerer and obtain access to your imported account at PO, you could send me a short note to the mail adress given in my profile. – Dilaton Jul 31 '14 at 10:20

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