2 citations · 3 across the 3 of their papers we have counts for
10 papers
A formula for the Gromov-Witten potential of an elliptic curve
Alexandr Buryak
An algorithm to determine all the Gromov-Witten invariants of any smooth projective curve was obtained by Okounkov and Pandharipande in 2006. They identified stationary invariants…
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…
Riemannian F-manifolds, bi-flat F-manifolds, and flat pencils of metrics
Alessandro Arsie, Alexandr Buryak, Paolo Lorenzoni +1
In this paper we study relations between various natural structures on F-manifolds. In particular, given an arbitrary Riemannian F-manifold we present a construction of a canonical…
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…