In this article,we consider the problem of lifting the GW theory of a symplectic divisor to that of the ambient manifold in the context of symplectic birational geometry.In particular,we generalizeMaulik-Pandharipande...In this article,we consider the problem of lifting the GW theory of a symplectic divisor to that of the ambient manifold in the context of symplectic birational geometry.In particular,we generalizeMaulik-Pandharipande’s relative/absolute correspondence to relative-divisor/absolute correspondence.Then,we use it to lift a minimal uniruled invariant of a divisor to that of the ambient manifold.展开更多
Motivated by Witten’s work,we propose a K-theoretic Verlinde/Grassmannian correspondence which relates the GL Verlinde numbers to the K-theoretic quasimap invariants of the Grassmannian.We recover these two types of ...Motivated by Witten’s work,we propose a K-theoretic Verlinde/Grassmannian correspondence which relates the GL Verlinde numbers to the K-theoretic quasimap invariants of the Grassmannian.We recover these two types of invariants by imposing different stability conditions on the gauged linear sigma model associated with the Grassmannian.We construct two families of stability conditions connecting the two theories and prove two wall-crossing results.We confirm the Verlinde/Grassmannian correspondence in the rank two case.展开更多
The authors prove that the total descendant potential functions of the theory of Fan-Jarvis-Ruan-Witten for D4 with symmetry group J and for D4T with symmetry group Gmax, respectively, are both tau-functions of the D4...The authors prove that the total descendant potential functions of the theory of Fan-Jarvis-Ruan-Witten for D4 with symmetry group J and for D4T with symmetry group Gmax, respectively, are both tau-functions of the D4 Kac-Wakimoto/Drinfeld-Sokolov hierarchy. This completes the proof, begun in the article by Fan-Jarvis-Ruan（2013）, of the Witten Integrable Hierarchies Conjecture for all simple（ADE） singularities.展开更多
This is a survey article for the mathematical theory of Witten's Gauged Linear Sigma Model, as developed recently by the authors. Instead of developing the theory in the most general setting, in this paper the aut...This is a survey article for the mathematical theory of Witten's Gauged Linear Sigma Model, as developed recently by the authors. Instead of developing the theory in the most general setting, in this paper the authors focus on the description of the moduli.展开更多
The gauged linear sigma model （GLSM for short） is a 2d quantum field theory introduced by Witten twenty years ago. Since then, it has been investigated extensively in physics by Hori and others. Recently, an algebro...The gauged linear sigma model （GLSM for short） is a 2d quantum field theory introduced by Witten twenty years ago. Since then, it has been investigated extensively in physics by Hori and others. Recently, an algebro-geometric theory （for both abelian and nonabelian GLSMs） was developed by the author and his collaborators so that he can start to rigorously compute its invariants and check against physical predications. The abelian GLSM was relatively better understood and is the focus of current mathematical investigation. In this article, the author would like to look over the horizon and consider the nonabelian GLSM. The nonabelian case possesses some new features unavailable to the ahelian GLSM. To aid the future mathematical development, the author surveys some of the key problems inspired by physics in the nonabelian GLSM.展开更多
文摘In this article,we consider the problem of lifting the GW theory of a symplectic divisor to that of the ambient manifold in the context of symplectic birational geometry.In particular,we generalizeMaulik-Pandharipande’s relative/absolute correspondence to relative-divisor/absolute correspondence.Then,we use it to lift a minimal uniruled invariant of a divisor to that of the ambient manifold.
基金The bulk of this work was done during the first author’s tenure at University of Michigan and he was partially supported by NSF grant DMS 1807079 and NSF FRG grant DMS 1564457.
文摘Motivated by Witten’s work,we propose a K-theoretic Verlinde/Grassmannian correspondence which relates the GL Verlinde numbers to the K-theoretic quasimap invariants of the Grassmannian.We recover these two types of invariants by imposing different stability conditions on the gauged linear sigma model associated with the Grassmannian.We construct two families of stability conditions connecting the two theories and prove two wall-crossing results.We confirm the Verlinde/Grassmannian correspondence in the rank two case.
基金supported by the National Natural Science Foundation of China(Nos.1132510111271028)+1 种基金the National Security Agency of USA(No.H98230-10-1-0181)the Doctoral Fund of the Ministry of Education of China(No.20120001110060)
文摘The authors prove that the total descendant potential functions of the theory of Fan-Jarvis-Ruan-Witten for D4 with symmetry group J and for D4T with symmetry group Gmax, respectively, are both tau-functions of the D4 Kac-Wakimoto/Drinfeld-Sokolov hierarchy. This completes the proof, begun in the article by Fan-Jarvis-Ruan（2013）, of the Witten Integrable Hierarchies Conjecture for all simple（ADE） singularities.
基金supported by the Natural Science Foundation(Nos.DMS-1564502,DMS-1405245,DMS-1564457)the National Natural Science Foundation of China(Nos.11325101,11271028)the Ph.D.Programs Foundation of Ministry of Education of China(No.20120001110060)
文摘This is a survey article for the mathematical theory of Witten's Gauged Linear Sigma Model, as developed recently by the authors. Instead of developing the theory in the most general setting, in this paper the authors focus on the description of the moduli.
基金supported by the Natural Science Foundation(Nos.DMS 1159265,DMS 1405245)
文摘The gauged linear sigma model （GLSM for short） is a 2d quantum field theory introduced by Witten twenty years ago. Since then, it has been investigated extensively in physics by Hori and others. Recently, an algebro-geometric theory （for both abelian and nonabelian GLSMs） was developed by the author and his collaborators so that he can start to rigorously compute its invariants and check against physical predications. The abelian GLSM was relatively better understood and is the focus of current mathematical investigation. In this article, the author would like to look over the horizon and consider the nonabelian GLSM. The nonabelian case possesses some new features unavailable to the ahelian GLSM. To aid the future mathematical development, the author surveys some of the key problems inspired by physics in the nonabelian GLSM.
