Fetching the paper…
Reading the bibliography…
For a simple Lie algebra $\mathfrak g$ we define a system of linear ODEs with polynomial coefficients, which we call the topological equation of $\mathfrak g$-type.
Kostant, B. (1959). The Principal Three-Dimensional Subgroup and the Betti Numbers of a Complex Simple Lie Group. American Journal of Mathematics: 973–1032
1959
Earlier work this paper cites.
Wasow, W. (1965) Asymptotic expansions for ordinary differential equations, Interscience Publishers, A Division of John Wiley and Sons Inc., New York - London - Sydney
1965
Earlier work this paper cites.
Kac, V. G. (1978). Infinite-dimensional algebras, Dedekind’s η \eta -function, classical Möbius function and the very strange formula. Advances in Mathematics, 30
1978
Earlier work this paper cites.
Drinfeld, V. G., Sokolov, V. V. (1985). Lie algebras and equations of Korteweg–de Vries type, J. Math. Sci. 30
1984
Earlier work this paper cites.
Heckman, G. J., Opdam, E. M. (1987). Root systems and hypergeometric functions. I. Compositio Mathematica, 64
1987
Earlier work this paper cites.
Kac, V. G., Wakimoto, M. (1989). Exceptional hierarchies of soliton equations. In Proceedings of symposia in pure mathematics (Vol. 49, p. 191)
1989
Earlier work this paper cites.
Balog, J., Fehér, L., O’Raifeartaigh, L., Forgacs, P., Wipf, A. (1990). Toda theory and W-algebra from a gauged WZNW point of view. Annals of Physics, 203
1990
Earlier work this paper cites.
Witten, E. (1991). Two-dimensional gravity and intersection theory on moduli space. Surveys in Diff. Geom., 1
1991
Earlier work this paper cites.
Witten, E. (1993). Algebraic geometry associated with matrix models of two-dimensional gravity (pp. 235–269). Topological methods in modern mathematics (Stony Brook, NY, 1991), Publish or Perish, Houston, TX
1991
Earlier work this paper cites.
Dijkgraaf, R. (1992) Intersection theory, integrable hierarchies and topological field theory. In: New Symmetry Principles in Quantum Field Theory, NATO ASI Series 295
1992
Earlier work this paper cites.
De Groot, M. F., Hollowood, T. J., Miramontes, J. L. (1992). Generalized Drinfel’d-Sokolov hierarchies. Communications in Mathematical Physics, 145
1992
Earlier work this paper cites.
Kontsevich, M. (1992). Intersection theory on the moduli space of curves and the matrix Airy function. Comm. Math. Phys., 147
1992
Earlier work this paper cites.
Witten, E. (1992) The N N matrix model and gauged WZW models. Nucl. Phys. B371
1992
Earlier work this paper cites.
Saito, K. (1993). On a linear structure of the quotient variety by a finite reflexion group. Publications of the Research Institute for Mathematical Sciences, 29
1993
Cited alongside, same era.
Kac, V. G. (1994). Infinite-dimensional Lie algebras (Vol. 44). Cambridge university press
1994
Cited alongside, same era.
Dubrovin, B. (1996). Geometry of 2D topological field theories. In “Integrable Systems and Quantum Groups”, Editors: Francaviglia, M., Greco, S. Springer Lecture Notes in Math. 1620
1996
Cited alongside, same era.
Dubrovin, B., Zhang, Y. (1998). Bihamiltonian hierarchies in 2D topological field theory at one-loop approximation. Communications in mathematical physics, 198
1998
Cited alongside, same era.
Dubrovin, B. (1999). Painlevé transcendents in two-dimensional topological field theory. In The Painlevé property (pp. 287–412). Springer New York
Faber, C., Shadrin, S., Zvonkine, D. (2010). Tautological relations and the r r -spin Witten conjecture. In Annales scientifiques de l’Ecole normale supérieure (Vol. 43, No. 4, pp. 621-658). Elsevier
2010
Later among the works it cites.
Liu, K., Xu, H. (2010). Descendent integrals and tautological rings of moduli spaces of curves. Geometry and Analysis Vol. 2, Adv. Lect. Math. 18
2010
Later among the works it cites.
Liu, K., Vakil, R., Xu, H. (2011). Formal pseudodifferential operators and Witten’s r r -spin numbers. Journal für die reine und angewandte Mathematik (Crelles Journal)
2011
Later among the works it cites.
Bakalov, B., Milanov, T. (2013). 𝒲 \mathcal{W} -constraints for the total descendant potential of a simple singularity. Compositio Mathematica, 149
2013
Later among the works it cites.
Fan, H., Jarvis, T., Ruan, Y. (2013). The Witten equation, mirror symmetry, and quantum singularity theory. Annals of Mathematics, 178
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
1999
Cited alongside, same era.
Dubrovin, B., Zhang, Y. (2001). Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov–Witten invariants. arXiv preprint arXiv: math/0108160
2001
Cited alongside, same era.
Givental, A. (2001). Gromov–Witten invariants and quantization of quadratic Hamiltonians. Mosc. Math. J, 1
2001
Cited alongside, same era.
Polishchuk, A., Vaintrob, A. (2001). Algebraic construction of Witten’s top Chern class. In: E. Previato (Ed.), Advances in Algebraic Geometry Motivated by Physics, AMS Special Session on Enumerative Geometry in Physics. Contemporary Mathematics 276
2001
Cited alongside, same era.
Jarvis, T. J., Kimura, T., Vaintrob, A. (2005). Spin Gromov–Witten invariants. Communications in mathematical physics, 259
2005
Cited alongside, same era.
Brézin, E., Hikami, S. (2007). Intersection numbers of Riemann surfaces from Gaussian matrix models. Journal of High Energy Physics, 2007
2007
Cited alongside, same era.
Dubrovin, B., Liu, S.-Q., Zhang, Y. (2008). Frobenius manifolds and central invariants for the Drinfeld–Sokolov biHamiltonian structures. Advances in Mathematics, 219
2008
Cited alongside, same era.
Brézin, E., Hikami, S. (2009). Computing topological invariants with one and two-matrix models. Journal of High Energy Physics, 2009
2009
Cited alongside, same era.
2013
Later among the works it cites.
Liu, S.-Q., Yang, D., Zhang, Y. (2013). Uniqueness Theorem of 𝒲 \mathcal{W} -Constraints for Simple Singularities. Letters in Mathematical Physics, 103
2013
Later among the works it cites.
Zhou, J. (2013). Solution of W-Constraints for R-Spin Intersection Numbers. arXiv: 1305.6991
2013
Later among the works it cites.
Liu, S.-Q., Ruan, Y., Zhang, Y. (2014). BCFG Drinfeld–Sokolov Hierarchies and FJRW-Theory. Inventiones Mathematicae. doi: 10.1007/s00222-014-0559-3
2014
Later among the works it cites.
Bertola, M., Dubrovin, B., Yang, D. (2015). Correlation functions of the KdV hierarchy and applications to intersection numbers over ℳ ¯ g , n . \overline{\mathcal{M}}_{g,n}. arXiv preprint arXiv: 1504.06452
2015
Closest in time.
2015
Closest in time.
Zhou, J. (2015). On absolute N-point function associated with Gelfand–Dickey polynomials. preprint
2015
Closest in time.
Zhou, J. (2015). Emergent geometry and mirror symmetry of a point. arXiv preprint arXiv: 1507.01679
2015
Closest in time.
Shadrin, S. V. (2003). Geometry of meromorphic functions and intersections onmoduli spaces of curves. International Mathematics Research Notices, 2003
2094
Closest in time.