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Hodge–GUE Correspondence and the Discrete KdV Equation
- B. Dubrovin, Si-Qi liu, Di Yang, You-jin Zhang
- MathematicsCommunications in Mathematical Physics
- 7 December 2016
We prove the conjectural relationship recently proposed in [9] between certain special cubic Hodge integrals of the Gopakumar--Mari\~no--Vafa type [17, 28] and GUE correlators, and the conjecture…
Generating series for GUE correlators
- B. Dubrovin, Di Yang
- Computer Science
- 26 April 2016
TLDR
The partition function of the extended r-reduced Kadomtsev–Petviashvili hierarchy
- M. Bertola, Di Yang
- Mathematics
- 20 November 2014
We derive a particular solution of the extended r-reduced KP hierarchy, which is specified by a generalized string equation . The work is a generalization to arbitrary r ≥ 2 ?> of Buryakʼs recent…
Classical Hurwitz numbers and related combinatorics
- B. Dubrovin, Di Yang, D. Zagier
- Mathematics
- 2016
In 1891 Hurwitz [30] studied the number Hg,d of genus g ≥ 0 and degree d ≥ 1 coverings of the Riemann sphere with 2g + 2d− 2 fixed branch points and in particular found a closed formula for Hg,d for…
Geometric interpretation of Zhou’s explicit formula for the Witten–Kontsevich tau function
Based on the work of Itzykson and Zuber on Kontsevich’s integrals, we give a geometric interpretation and a simple proof of Zhou’s explicit formula for the Witten–Kontsevich tau function. More…
Simple Lie algebras and topological ODEs
- M. Bertola, B. Dubrovin, Di Yang
- Mathematics
- 15 August 2015
For a simple Lie algebra $\mathfrak g$ we define a system of linear ODEs with polynomial coefficients, which we call the topological equation of $\mathfrak g$-type. The dimension of the space of…
Matrix Resolvent and the Discrete KdV Hierarchy
- B. Dubrovin, Di Yang
- Mathematics
- 27 March 2019
Based on the matrix-resolvent approach, for an arbitrary solution to the discrete KdV hierarchy, we define the tau-function of the solution, and compare it with another tau-function of the solution…
Correlation functions of the KdV hierarchy and applications to intersection numbers over M¯g,n
- M. Bertola, B. Dubrovin, Di Yang
- Mathematics
- 24 April 2015
Hodge integrals and tau-symmetric integrable hierarchies of Hamiltonian evolutionary PDEs
- B. Dubrovin, Si-Qi liu, Di Yang, You-jin Zhang
- Mathematics
- 16 September 2014
On tau-functions for the KdV hierarchy
- B. Dubrovin, Di Yang, D. Zagier
- Mathematics
- 20 December 2018
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 via algebraic…
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