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On the strong DR/DZ equivalence conjecture

Xavier Blot, Danilo Lewański and Sergey Shadrin

Geometry & Topology 30 (2026) 3333–3359
Bibliography
1 A Alexandrov, F Hernández Iglesias, S Shadrin, Buryak–Okounkov formula for the n-point function and a new proof of the Witten conjecture, Int. Math. Res. Not. 2021 (2021) 14296 MR4320810
2 A Arsie, A Buryak, P Lorenzoni, P Rossi, Flat F-manifolds, F-CohFTs, and integrable hierarchies, Comm. Math. Phys. 388 (2021) 291 MR4328055
3 X Blot, D Lewański, S Shadrin, Rooted trees with level structures, Ω-classes and double ramification cycles, (2024) arXiv:2406.06205
4 X Blot, D Lewański, P Rossi, S Shadrin, Stable tree expressions with omega-classes and double ramification cycles, J. Geom. Phys. 209 (2025) 105391 MR4839088
5 X Blot, A Sauvaget, S Shadrin, The master relation for polynomiality and equivalences of integrable systems, Bull. Lond. Math. Soc. 57 (2025) 599 MR4861898
6 A Buryak, Double ramification cycles and integrable hierarchies, Comm. Math. Phys. 336 (2015) 1085 MR3324138
7 A Buryak, P Rossi, Double ramification cycles and quantum integrable systems, Lett. Math. Phys. 106 (2016) 289 MR3462029
8 A Buryak, P Rossi, Recursion relations for double ramification hierarchies, Comm. Math. Phys. 342 (2016) 533 MR3459159
9 A Buryak, P Rossi, Extended r-spin theory in all genera and the discrete KdV hierarchy, Adv. Math. 386 (2021) 107794 MR4265543
10 A Buryak, S Shadrin, Tautological relations and integrable systems, Épijournal Géom. Algébrique 8 (2024) 12 MR4801091
11 A Buryak, H Posthuma, S Shadrin, On deformations of quasi-Miura transformations and the Dubrovin–Zhang bracket, J. Geom. Phys. 62 (2012) 1639 MR2922026
12 A Buryak, H Posthuma, S Shadrin, A polynomial bracket for the Dubrovin–Zhang hierarchies, J. Differential Geom. 92 (2012) 153 MR2998900
13 A Buryak, S Shadrin, L Spitz, D Zvonkine, Integrals of ψ-classes over double ramification cycles, Amer. J. Math. 137 (2015) 699 MR3357119
14 A Buryak, B Dubrovin, J Guéré, P Rossi, Tau-structure for the double ramification hierarchies, Comm. Math. Phys. 363 (2018) 191 MR3849988
15 A Buryak, J Guéré, P Rossi, DR/DZ equivalence conjecture and tautological relations, Geom. Topol. 23 (2019) 3537 MR4059088
16 A Buryak, B Dubrovin, J Guéré, P Rossi, Integrable systems of double ramification type, Int. Math. Res. Not. 2020 (2020) 10381 MR4190406
17 A Buryak, P Rossi, S Shadrin, Towards a bihamiltonian structure for the double ramification hierarchy, Lett. Math. Phys. 111 (2021) 13 MR4212875
18 A Buryak, F Hernández Iglesias, S Shadrin, A conjectural formula for DRg(a,−a)λg, Épijournal Géom. Algébrique 6 (2022) 8 MR4443301
19 B Dubrovin, Y Zhang, Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov–Witten invariants, (2001) arXiv:math/0108160
20 C Faber, S Shadrin, D Zvonkine, Tautological relations and the r-spin Witten conjecture, Ann. Sci. Éc. Norm. Supér. (4) 43 (2010) 621 MR2722511
21 T Graber, R Pandharipande, Constructions of nontautological classes on moduli spaces of curves, Michigan Math. J. 51 (2003) 93 MR1960923
22 D Gubarevich, A conjectural formula for λgDRg(a,−a) is true in Gorenstein quotient, (2022) arXiv:2204.05396
23 M Kontsevich, Intersection theory on the moduli space of curves and the matrix Airy function, Comm. Math. Phys. 147 (1992) 1 MR1171758
24 M Kontsevich, Y Manin, Gromov–Witten classes, quantum cohomology, and enumerative geometry, Comm. Math. Phys. 164 (1994) 525 MR1291244
25 X Liu, C Wang, On a tautological relation conjectured by Buryak and Shadrin, Sci. China Math. 69 (2026) 285 MR5012765
26 S Q Liu, Z Wang, Y Zhang, Linearization of Virasoro symmetries associated with semisimple Frobenius manifolds, Adv. Math. 460 (2025) 110046 MR4831844
27 R Pandharipande, A Pixton, D Zvonkine, Relations on ℳg,n via 3-spin structures, J. Amer. Math. Soc. 28 (2015) 279 MR3264769
28 C Teleman, The structure of 2D semi-simple field theories, Invent. Math. 188 (2012) 525 MR2917177
29 E Witten, Two-dimensional gravity and intersection theory on moduli space, from: "Surveys in differential geometry", Lehigh Univ., Bethlehem, PA (1991) 243 MR1144529
30 E Witten, Algebraic geometry associated with matrix models of two-dimensional gravity, from: "Topological methods in modern mathematics" (editors L R Goldberg, A V Phillips), Publish or Perish, Houston, TX (1993) 235 MR1215968