Witten's \(D_4\) integrable hierarchies conjecture

DOI10.1007/s11401-016-0944-xzbMath1342.14110arXiv1008.0927OpenAlexW2964118752WikidataQ122975729 ScholiaQ122975729MaRDI QIDQ266178

Huijun Fan, Yongbin Ruan, Evan Merrell, Amanda E. Francis, Tyler J. Jarvis

Publication date: 13 April 2016

Published in: Chinese Annals of Mathematics. Series B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1008.0927

zbMATH Keywords

quantum cohomologyintegrable hierarchiessingularity theoryFrobenius manifolds

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) (14N35) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) Gromov-Witten invariants, quantum cohomology, Frobenius manifolds (53D45) Local complex singularities (32S05)

Related Items

Landau-Ginzburg mirror symmetry conjecture, Punctures and \(p\)-spin curves from matrix models. III: \(D_l\) type and logarithmic potential, A global mirror symmetry framework for the Landau-Ginzburg/Calabi-Yau correspondence, Uniqueness theorem of \(\mathcal W\)-constraints for simple singularities, On the genus two free energies for semisimple Frobenius manifolds, Geometry and arithmetic of integrable hierarchies of KdV type. I: Integrality, Quantum \(D_4\) Drinfeld-Sokolov hierarchy and quantum singularity theory, BCFG Drinfeld-Sokolov hierarchies and FJRW-theory, Tau-structure for the double ramification hierarchies, Borodin-Okounkov formula, string equation and topological solutions of Drinfeld-Sokolov hierarchies, On the Drinfeld-Sokolov hierarchy of type \(E_6^{(1)}\) and its topological solution, Torsion type invariants of singularities, Simple Lie algebras, Drinfeld--Sokolov hierarchies, and multi-point correlation functions, Borcea-Voisin mirror symmetry for Landau-Ginzburg models, Fredholm Pfaffian \(\tau \)-functions for orthogonal isospectral and isomonodromic systems

Uses Software

• SageMath
• MgnF

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Witten equation, mirror symmetry, and quantum singularity theory
• Soliton equations, vertex operators, and simple singularities
• Intersection numbers and rank one cohomological field theories in genus one
• Calculating cohomology groups of moduli spaces of curves via algebraic geometry
• Tautological relations and the $r$-spin Witten conjecture
• Towards an enumerative geometry of the moduli space of twisted curves and rth roots
• A Second note on Symmetry of Singularities
• A Note on Symmetry of Singularities
• CORRELATION FUNCTIONS FOR TOPOLOGICAL LANDAU-GINZBURG MODELS WITH c≤3