147 citations · 935 across the 73 of their papers we have counts for
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Simple Lie algebras and topological ODEs
Marco Bertola, Boris Dubrovin, Di Yang
For a simple Lie algebra we define a system of linear ODEs with polynomial coefficients, which we call the topological equation of -type. The dimension o…
Symplectic geometry of the moduli space of projective structures in homological coordinates
Marco Bertola, Dmitry Korotkin, Chaya Norton
We introduce a natural symplectic structure on the moduli space of quadratic differentials with simple zeros and describe its Darboux coordinate systems in terms of so-called homol…
Hankel Determinant Approach to Generalized Vorob'ev-Yablonski Polynomials and their Roots
Ferenc Balogh, Marco Bertola, Thomas Bothner
Generalized Vorob'ev-Yablonski polynomials have been introduced by Clarkson and Mansfield in their study of rational solutions of the second Painlevé hierarchy. We present new Hank…
Correlation functions of the KdV hierarchy and applications to intersection numbers over
Marco Bertola, Boris Dubrovin, Di Yang
We derive an explicit generating function of correlations functions of an arbitrary tau-function of the KdV hierarchy. In particular applications, our formulation gives closed form…