15 citations · 49 across the 14 of their papers we have counts for
14 papers
Mirror Symmetry of the Affine Toda Systems
Xin Jin, Zhiwei Yun
For a complex reductive group , we prove a homological mirror symmetry between the wrapped Fukaya category of the affine Toda system for and coherent sheaves on the regular…
Cohomology of the universal centralizers I: the adjoint group case
Xin Jin
We compute the rational cohomology of the universal centralizer (also known as the Toda system or BFM space) for a complex (connected) semisimple group of adjoint form. W…
Homological Mirror Symmetry for the universal centralizers
Xin Jin
We prove homological mirror symmetry for the universal centralizer (a.k.a the Toda space), associated to any complex reductive Lie group . The A-side is a partially wrappe…
Homoclinic and heteroclinic intersections for lemon billiards
Xin Jin, Pengfei Zhang
We study the dynamical billiards on a symmetric lemon table , where is the intersection of two unit disks with center distance . We show that th…
Birkhoff Normal Form and Twist Coefficients of Periodic Orbits of Billiards
Xin Jin, Pengfei Zhang
In this paper we study the Birkhoff Normal Form around elliptic periodic points for a variety of dynamical billiards. We give an explicit construction of the Birkhoff transformatio…
Homological Mirror Symmetry for the universal centralizers I: The adjoint group case
Xin Jin
We prove homological mirror symmetry for the universal centralizer (a.k.a Toda space), associated to any complex semisimple Lie group . The A-side is a partially wrapped F…
Microlocal sheaf categories and the -homomorphism
Xin Jin
Let be a smooth manifold and be a commutative (or at least ) ring spectrum. Given a smooth exact Lagrangian , the microlocal s…
Hyperbolicity of asymmetric lemon billiards
Xin Jin, Pengfei Zhang
Asymmetric lemon billiards was introduced in [CMZZ], where the billiard table is the intersection of two round disks with radii , respectively, and measures…
A Hamiltonian -action, stratified Morse theory and the -homomorphism
Xin Jin
We use sheaves of spectra to quantize a Hamiltonian -action on that naturally arises from Bott periodicity. We employ…
Brane structures in microlocal sheaf theory
Xin Jin, David Treumann
Let be an exact Lagrangian submanifold of a cotangent bundle , asymptotic to a Legendrian submanifold . We study a locally constant sheaf of $\inf…
Representing the big tilting sheaves as holomorphic Morse branes
Xin Jin
We introduce Morse branes in the Fukaya category of a holomorphic symplectic manifold, with the goal of constructing tilting objects in the category. We give a construction of a cl…
Symplectomorphism group of and the braid group I: a homotopy equivalence for
Xin Jin
For a semisimple Lie group over , we study the homotopy type of the symplectomorphism group of the cotangent bundle of the flag variety and its relation…
Holomorphic Lagrangian branes correspond to perverse sheaves
Xin Jin
Let X be a compact complex manifold, be the bounded derived category of constructible sheaves on , and be the Fukaya category of . A Lagrangian bran…
Trivariate monomial complete intersections and plane partitions
Charles Chen, Alan Guo, Xin Jin +1
We consider the homogeneous components U_r of the map on R = k[x,y,z]/(x^A, y^B, z^C) that multiplies by x + y + z. We prove a relationship between the Smith normal forms of submat…