Computing a categorical Gromov-Witten invariant


主讲人:涂君武 上海科技大学 副教授、研究员





2001-2005 南京大学数学系, 本科 2005-2011 威斯康星大学数学系, 博士 2011-2014 俄勒冈大学数学系,博士后 2014-2018 密苏里大学数学系,助理教授 2018-现在 上海科技大学数学科学研究所,副教授


We compute the g = 1, n = 1 B-model Gromov-Witten invariant of an elliptic curve E directly from the derived category of coherent sheaves on E. More precisely, we carry out the computation of the categorical Gromov-Witten invariant defined by Costello using as target a cyclic A-infinity model due to Polishchuk. This is the first non-trivial computation of a positive genus categorical GromovWitten invariant, and the result agrees with the prediction of mirror symmetry: it matches the classical (non-categorical) Gromov-Witten invariants of a symplectic 2-torus computed by Dijkgraaf. This is a joint work with Andrei Caldararu.

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