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Deformations of the Riemann hierarchy and the geometry of
Alexandr Buryak, Paolo Rossi
The Riemann hierarchy is the simplest example of rank one, (+)-dimensional integrable system of nonlinear evolutionary PDEs. It corresponds to the dispersionless limit of the…
The bihamiltonian structures of the DR/DZ hierarchies at the approximation up to genus one
Oscar Brauer, Alexandr Buryak
In a recent paper, giving an arbitrary homogeneous cohomological field theory (CohFT), Rossi, Shadrin, and the first author proposed a simple formula for a bracket on the space loc…
Flat F-manifolds, F-CohFTs, and integrable hierarchies
Alessandro Arsie, Alexandr Buryak, Paolo Lorenzoni +1
We define the double ramification hierarchy associated to an F-cohomological field theory and use this construction to prove that the principal hierarchy of any semisimple (homogen…
Open r-spin theory I: Foundations
Alexandr Buryak, Emily Clader, Ran J. Tessler
We lay the foundation for a version of -spin theory in genus zero for Riemann surfaces with boundary. In particular, we define the notion of -spin disks, their moduli space,…
Open Saito theory for and singularities
Alexey Basalaev, Alexandr Buryak
A well known construction of B. Dubrovin and K. Saito endows the parameter space of a universal unfolding of a simple singularity with a Frobenius manifold structure. In our paper…
Open WDVV equations and Virasoro constraints
Alexey Basalaev, Alexandr Buryak
In their fundamental work, B. Dubrovin and Y. Zhang, generalizing the Virasoro equations for the genus 0 Gromov-Witten invariants, proved the Virasoro equations for a descendent po…