Xin Jin

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20202026

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math.SG2026

Mirror Symmetry of the Affine Toda Systems

Xin Jin, Zhiwei Yun

For a complex reductive group $G$ , we prove a homological mirror symmetry between the wrapped Fukaya category of the affine Toda system for $G$ and coherent sheaves on the regular…

math.SG2021

Homological Mirror Symmetry for the universal centralizers I: The adjoint group case

Xin Jin

We prove homological mirror symmetry for the universal centralizer $J_{G}$ (a.k.a Toda space), associated to any complex semisimple Lie group $G$ . The A-side is a partially wrapped F…

math.SG2020

Microlocal sheaf categories and the $J$ -homomorphism

Xin Jin

Let $X$ be a smooth manifold and $k$ be a commutative (or at least $E_{2}$ ) ring spectrum. Given a smooth exact Lagrangian $L ↪ T^{*} X$ , the microlocal s…

Mirror Symmetry of the Affine Toda Systems

Homological Mirror Symmetry for the universal centralizers I: The adjoint group case

Microlocal sheaf categories and the J-homomorphism

Microlocal sheaf categories and the $J$ -homomorphism