@article {cotti2019,
	title = {Isomonodromy deformations at an irregular singularity with coalescing eigenvalues},
	journal = {Duke Math. J.},
	volume = {168},
	number = {6},
	year = {2019},
	month = {04},
	pages = {967{\textendash}1108},
	publisher = {Duke University Press},
	abstract = {<p>We consider an n{\texttimes}n linear system of ODEs with an irregular singularity of Poincar\'e rank 1 at z=$\infty$, holomorphically depending on parameter t within a polydisc in Cn centred at t=0. The eigenvalues of the leading matrix at z=$\infty$ coalesce along a locus Δ contained in the polydisc, passing through t=0. Namely, z=$\infty$ is a resonant irregular singularity for t∈Δ. We analyse the case when the leading matrix remains diagonalisable at Δ. We discuss the existence of fundamental matrix solutions, their asymptotics, Stokes phenomenon and monodromy data as t varies in the polydisc, and their limits for t tending to points of Δ. When the deformation is isomonodromic away from Δ, it is well known that a fundamental matrix solution has singularities at Δ. When the system also has a Fuchsian singularity at z=0, we show under minimal vanishing conditions on the residue matrix at z=0 that isomonodromic deformations can be extended to the whole polydisc, including Δ, in such a way that the fundamental matrix solutions and the constant monodromy data are well defined in the whole polydisc. These data can be computed just by considering the system at fixed t=0. Conversely, if the t-dependent system is isomonodromic in a small domain contained in the polydisc not intersecting Δ, if the entries of the Stokes matrices with indices corresponding to coalescing eigenvalues vanish, then we show that Δ is not a branching locus for the fundamental matrix solutions. The importance of these results for the analytic theory of Frobenius Manifolds is explained. An application to Painlev\'e equations is discussed.</p>},
	doi = {10.1215/00127094-2018-0059},
	url = {https://doi.org/10.1215/00127094-2018-0059},
	author = {Giordano Cotti and Boris Dubrovin and Davide Guzzetti}
}
@article {2001,
	title = {Inverse Problem and Monodromy Data for Three-Dimensional Frobenius Manifolds},
	journal = {Mathematical Physics, Analysis and Geometry 4: 245{\textendash}291, 2001},
	year = {2001},
	publisher = {RIMS, Kyoto University},
	abstract = {We study the inverse problem for semi-simple Frobenius manifolds of dimension 3 and we\r\nexplicitly compute a parametric form of the solutions of theWDVV equations in terms of Painlev{\'e} VI\r\ntranscendents. We show that the solutions are labeled by a set of monodromy data. We use our parametric\r\nform to explicitly construct polynomial and algebraic solutions and to derive the generating\r\nfunction of Gromov{\textendash}Witten invariants of the quantum cohomology of the two-dimensional projective\r\nspace. The procedure is a relevant application of the theory of isomonodromic deformations.},
	keywords = {Frobenius Manifolds, Painleve Equations, Isomonodromy deformations},
	doi = {10.1023/A:1012933622521},
	author = {Davide Guzzetti}
}
@article {2000,
	title = {Inverse problem for Semisimple Frobenius Manifolds Monodromy Data and the Painlev{\'e} VI Equation},
	number = {SISSA;101/00/FM},
	year = {2000},
	publisher = {SISSA Library},
	url = {http://hdl.handle.net/1963/1557},
	author = {Davide Guzzetti}
}
