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Open intersection numbers and the wave function of the KdV hierarchy
  • A. Buryak
  • Mathematics, Physics
  • 28 September 2014
Recently R. Pandharipande, J. Solomon and R. Tessler initiated a study of the intersection theory on the moduli space of Riemann surfaces with boundary. They conjectured that the generating series ofExpand
Double Ramification Cycles and Integrable Hierarchies
In this paper we present a new construction of a hamiltonian hierarchy associated to a cohomological field theory. We conjecture that in the semisimple case our hierarchy is related to theExpand
Matrix Models and A Proof of the Open Analog of Witten’s Conjecture
In a recent work, R. Pandharipande, J. P. Solomon and the second author have initiated a study of the intersection theory on the moduli space of Riemann surfaces with boundary. They conjectured thatExpand
On deformations of quasi-Miura transformations and the Dubrovin–Zhang bracket
Abstract In our recent paper, we proved the polynomiality of a Poisson bracket for a class of infinite-dimensional Hamiltonian systems of partial differential equations (PDEs) associated toExpand
A polynomial bracket for the Dubrovin--Zhang hierarchies
We define a hierarchy of Hamiltonian PDEs associated to an arbitrary tau-function in the semi-simple orbit of the Givental group action on genus expansions of Frobenius manifolds. We prove that theExpand
A Remark on Deformations of Hurwitz Frobenius Manifolds
In this note, we use the formalism of multi-KP hierarchies in order to give some general formulas for infinitesimal deformations of solutions of the Darboux–Egoroff system. As an application, weExpand
Closed extended $r$-spin theory and the Gelfand-Dickey wave function
We study a generalization of genus-zero $r$-spin theory in which exactly one insertion has a negative-one twist, which we refer to as the "closed extended" theory, and which is closely related to theExpand
Open WDVV equations and Virasoro constraints.
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 potential in genus 0Expand
Double Ramification Cycles and Quantum Integrable Systems
In this paper, we define a quantization of the Double Ramification Hierarchies of Buryak (Commun Math Phys 336:1085–1107, 2015) and Buryak and Rossi (Commun Math Phys, 2014), using intersectionExpand
Top tautological group of Mg,n
We describe the structure of the top tautological group in the cohomology of the moduli space of smooth genus g curves with n marked points.