On the strong DR/DZ equivalence conjecture

Blot, Xavier; Lewański, Danilo; Shadrin, Sergey

doi:10.2140/gt.2026.30.3333

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On the strong DR/DZ equivalence conjecture

Xavier Blot, Danilo Lewański and Sergey Shadrin

Geometry & Topology 30 (2026) 3333–3359

DOI: 10.2140/gt.2026.30.3333

Abstract

We establish the Miura equivalence between two integrable hierarchies associated to a semisimple cohomological field theory: the double ramification hierarchy of Buryak and the Dubrovin–Zhang hierarchy. This equivalence was conjectured by Buryak and further refined by Buryak, Dubrovin, Guéré, and Rossi.

Keywords

integrable systems, moduli of curves, DR/DZ equivalence, tautological relations, Miura equivalence

Mathematical Subject Classification

Primary: 14H10, 37K10

References

Publication

Received: 18 September 2024

Revised: 15 December 2025

Accepted: 13 May 2026

Published: 12 October 2026

Proposed: Yakov Eliashberg

Seconded: Mark Gross, Arend Bayer

Authors

Xavier Blot
Korteweg-de Vriesinstituut voor Wiskunde University of Amsterdam Amsterdam Netherlands

Danilo Lewański
Department of Mathematics, Informatics and Geosciences University of Trieste Trieste Italy

Sergey Shadrin
Korteweg-de Vriesinstituut voor Wiskunde University of Amsterdam Amsterdam Netherlands

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Volume 30, issue 9 (2026)