IBS - Symplectic Monday SeminarㅣEquivariant Homological Mirror Symmetry for CP1

The mirror of an n-dimensional toric Fano manifold X is known to be (C∗)n(C∗)n equipped with a Laurent polynomial f and is called the Landau-Ginzburg model. The homological mirror symmetry for toric Fano manifold says that the Fukaya category of XX is equivalent to the category of matrix factorizations of ff (Cho, Hong and Lau 2019). Givental introduced the equivariant Landau-Ginzburg mirror FF by adding logarithmic terms to ff. In this talk we formulate and show a version of equivariant homological mirror symmetry for CP1CP1 by introducing equivariant Floer A∞A∞ algebra for toric fibers. This is a joint work with Fumihiko Sanda (Gakushuin University) and is based on our preprint https://arxiv.org/abs/2112.14622 .