Gromov-Witten invariants of Calabi-Yau A-infinity categories

来源 :2017-2018年复旦大学数学学科青年学者论坛 | 被引量 : 0次 | 上传用户:kxdn01
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  Classical mirror symmetry relates Gromov-Witten invariants in symplectic geometry to Yukawa coupling invariants in algebraic geometry.Through non-commutative Hodge theory,one can define categorical Gromov-Witten invariants associated to(Calabi-Yau A-infinity)categories.Conjecturally,this construction should reproduce the Gromov-Witten invariants and Yukawa coupling invariants,when applied Fukaya categories and Derived categories,respectively.In this talk,I describe a first computation of categorical Gromov-Witten invariants at positive genus.This is a joint work with Andrei Caldararu.
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