Abstract:
The main goal of the paper is to show that the DR hierarchies, introduced by the author in an earlier paper, allow one to establish, in the most clear way, a relation between the topology of the Deligne–Mumford compactification $\overline {\mathcal M}_{g,n}$ of the moduli space $\mathcal M_{g,n}$ of smooth algebraic curves of genus $g$ with $n$ marked points and integrable systems of mathematical physics. We will also discuss a promising approach given by the theory of DR hierarchies to the solution of a general problem in the area of Witten-type conjectures, namely, to the proof of the existence of a Dubrovin–Zhang hierarchy for an arbitrary cohomological field theory.
This work was supported by the Russian Science Foundation under grant no. 20-71-10110, https://rscf.ru/en/project/20-71-10110/, and performed at the P. G. Demidov Yaroslavl State University.
Citation:
A. Yu. Buryak, “DR Hierarchies: From the Moduli Spaces of Curves to Integrable Systems”, Geometry, Topology, and Mathematical Physics, Collected papers. Dedicated to Academician Sergei Petrovich Novikov on the occasion of his 85th birthday, Trudy Mat. Inst. Steklova, 325, Steklov Mathematical Institute of RAS, Moscow, 2024, 26–66; Proc. Steklov Inst. Math., 325 (2024), 21–59
\Bibitem{Bur24}
\by A.~Yu.~Buryak
\paper DR Hierarchies: From the Moduli Spaces of Curves to Integrable Systems
\inbook Geometry, Topology, and Mathematical Physics
\bookinfo Collected papers. Dedicated to Academician Sergei Petrovich Novikov on the occasion of his 85th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2024
\vol 325
\pages 26--66
\publ Steklov Mathematical Institute of RAS
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4409}
\crossref{https://doi.org/10.4213/tm4409}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2024
\vol 325
\pages 21--59
\crossref{https://doi.org/10.1134/S0081543824020020}
Citation in format AMSBIB
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