42 citations · 70 across the 12 of their papers we have counts for
6 papers · 1 filter
On tau-functions for the KdV hierarchy
Boris Dubrovin, Di Yang, Don Zagier
For an arbitrary solution to the KdV hierarchy, the generating series of logarithmic derivatives of the tau-function of the solution can be expressed by the basic matrix resolvent…
Helix Structures in Quantum Cohomology of Fano Varieties
Giordano Cotti, Boris Dubrovin, Davide Guzzetti
In this paper we consider a conjecture formulated by the second author in occasion of the 1998 ICM in Berlin (arXiv:math/9807034v2). This conjecture states the equivalence, for a F…
A Riemann-Hilbert Approach to the Heun Equation
Boris Dubrovin, Andrei Kapaev
We describe the close connection between the linear system for the sixth Painlevé equation and the general Heun equation, formulate the Riemann-Hilbert problem for the Heun functio…
Algebraic spectral curves over and their tau-functions
Boris Dubrovin
Let be a matrix polynomial with rational coefficients. Denote the spectral curve . Under some natural assumptions a…
Approximating tau-functions by theta-functions
Boris Dubrovin
We prove that the logarithm of an arbitrary tau-function of the KdV hierarchy can be approximated, in the topology of graded formal series by the logarithmic expansions of hyperell…
Gromov--Witten invariants of the Riemann sphere
Boris Dubrovin, Di Yang, Don Zagier
A conjectural formula for the -point generating function of Gromov--Witten invariants of the Riemann sphere for all genera and all degrees was proposed in \cite{DY2}. In this pa…