He is also interested in the connections of his main research topics with algebraic geometry and dynamical systems.
[1] In 2017, with Gábor Székelyhidi and Ben Weinkove, Valentino Tosatti proved a conjecture published in 1984 by Paul Gauduchon.
[4][5] Acta Mathematica published their proof that on n-dimensional compact complex manifolds there is always a Gauduchon metric with prescribed volume form.
For this purpose, the behavior of a large class of elliptic nonlinear partial differential equations of second order on Hermitian manifolds had to be investigated.
In 2019, he was elected a Fellow of the American Mathematical Society for "contributions in geometric analysis and complex geometry".