Symplectic geometry is a branch of differential geometry and differential topology and has its origins in the Hamiltonian formulation of classical mechanics.In the last few decades,symplectic geometry has experienced ...Symplectic geometry is a branch of differential geometry and differential topology and has its origins in the Hamiltonian formulation of classical mechanics.In the last few decades,symplectic geometry has experienced enormous progress and has had interactions with many other branches of mathematics,including enumerative geometry,low-dimensional topology,mathematical physics,Hamiltonian dynamics,integrable systems etc..展开更多
By employing EQ^(ROT)_(1) nonconforming finite element,the numerical approximation is presented for multi-term time-fractional mixed sub-diffusion and diffusion-wave equation on anisotropic meshes.Comparing with the m...By employing EQ^(ROT)_(1) nonconforming finite element,the numerical approximation is presented for multi-term time-fractional mixed sub-diffusion and diffusion-wave equation on anisotropic meshes.Comparing with the multi-term time-fractional sub-diffusion equation or diffusion-wave equation,the mixed case contains a special time-space coupled derivative,which leads to many difficulties in numerical analysis.Firstly,a fully discrete scheme is established by using nonconforming finite element method(FEM)in spatial direction and L1 approximation coupled with Crank-Nicolson(L1-CN)scheme in temporal direction.Furthermore,the fully discrete scheme is proved to be unconditional stable.Besides,convergence and superclose results are derived by using the properties of EQ^(ROT)_(1) nonconforming finite element.What's more,the global superconvergence is obtained via the interpolation postprocessing technique.Finally,several numerical results are provided to demonstrate the theoretical analysis on anisotropic meshes.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 concept of tt^(*)geometric structure was introduced by physicists(see[4,9]and references therein),and then studied firstly in mathematics by C.Hertling[26].It is believed that the tt*geometric structure contains t...The concept of tt^(*)geometric structure was introduced by physicists(see[4,9]and references therein),and then studied firstly in mathematics by C.Hertling[26].It is believed that the tt*geometric structure contains the whole genus 0 information of a two dimensional topological field theory.In this paper,we propose the LG/CY correspondence conjecture for tt^(*)geome-try and obtain the following result.Let f∈￠[z_(0),…,z_(n+1)]be a nondegenerate homogeneous polynomial of degree n+2,then it defines a Calabi-Yau model represented by a Calabi-Yau hypersurface X_(f)in(￠P)^(n+1)or a Landau-Ginzburg model represented by a hypersurface singularity(￠^(n+2),f),both can be written as a tt^(*)structure.We proved that there exists a tt^(*)substructure on Landau-Ginzburg side,which should correspond to the tt*structure from variation of Hodge structures in Calabi-Yau side.We build the isomorphism of almost all structures in tt^(*)geometries between these two models except the isomorphism between real structures.展开更多
文摘Symplectic geometry is a branch of differential geometry and differential topology and has its origins in the Hamiltonian formulation of classical mechanics.In the last few decades,symplectic geometry has experienced enormous progress and has had interactions with many other branches of mathematics,including enumerative geometry,low-dimensional topology,mathematical physics,Hamiltonian dynamics,integrable systems etc..
基金National Natural Science Foundation of China(No.11971416)Scientific Research Innovation Team of Xuchang University(No.2022CXTD002)+3 种基金Foundation for University Key Young Teacher of Henan Province(No.2019GGJS214)Key Scientific Research Projects in Universities of Henan Province(Nos.21B110007,22A110022)National Natural Science Foundation of China(International cooperation key project:No.12120101001)Australian Research Council via the Discovery Project(DP190101889).
文摘By employing EQ^(ROT)_(1) nonconforming finite element,the numerical approximation is presented for multi-term time-fractional mixed sub-diffusion and diffusion-wave equation on anisotropic meshes.Comparing with the multi-term time-fractional sub-diffusion equation or diffusion-wave equation,the mixed case contains a special time-space coupled derivative,which leads to many difficulties in numerical analysis.Firstly,a fully discrete scheme is established by using nonconforming finite element method(FEM)in spatial direction and L1 approximation coupled with Crank-Nicolson(L1-CN)scheme in temporal direction.Furthermore,the fully discrete scheme is proved to be unconditional stable.Besides,convergence and superclose results are derived by using the properties of EQ^(ROT)_(1) nonconforming finite element.What's more,the global superconvergence is obtained via the interpolation postprocessing technique.Finally,several numerical results are provided to demonstrate the theoretical analysis on anisotropic meshes.
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 NSFC(11271028,11325101,11671033,11831017,11890660,11890661)
文摘The concept of tt^(*)geometric structure was introduced by physicists(see[4,9]and references therein),and then studied firstly in mathematics by C.Hertling[26].It is believed that the tt*geometric structure contains the whole genus 0 information of a two dimensional topological field theory.In this paper,we propose the LG/CY correspondence conjecture for tt^(*)geome-try and obtain the following result.Let f∈￠[z_(0),…,z_(n+1)]be a nondegenerate homogeneous polynomial of degree n+2,then it defines a Calabi-Yau model represented by a Calabi-Yau hypersurface X_(f)in(￠P)^(n+1)or a Landau-Ginzburg model represented by a hypersurface singularity(￠^(n+2),f),both can be written as a tt^(*)structure.We proved that there exists a tt^(*)substructure on Landau-Ginzburg side,which should correspond to the tt*structure from variation of Hodge structures in Calabi-Yau side.We build the isomorphism of almost all structures in tt^(*)geometries between these two models except the isomorphism between real structures.
