I've loved mathematics for as long as I can remember, or at least since I was first introduced to it, when I was six. Although I couldn’t explain that feeling at the time, my curiosity about the world has always fueled my passion. Today, I am pursuing a degree in mathematics and about to begin my thesis in differential geometry, under the supervision of Dr. Adrián Andrada. His guidance has been central in developing my interest in this field, especially in complex geometry—an area in which I deeply admire his contribution and dedication.
Participating in the Hong Kong Laureate Forum represents an extraordinary opportunity to connect with leading scientists whose journeys reflect a lifetime of discovery. I’m particularly excited to meet Sir Nigel Hitchin, whose work in geometry has greatly inspired my academic path. Learning from his experience would be truly motivating as I take my first steps into research.
I believe science is not only about solving problems but also about building bridges between cultures and generations. The Forum’s mission resonates with my goals as a developing mathematician. I see HKLF 2025 as a key starting point for my scientific career and look forward to it with great enthusiasm.

Academic_Transcript_Uni_EN.pdf.pdf

Dr. Adrian Andrada - Universidad Nacional de Córdoba

Dra. Maria Laura Barberis - Universidad Nacional de Córdoba

Letter_Chaves_Valentina_Barberis.pdf

My research focuses on computing the de Rham cohomology of nilmanifolds and solvmanifolds equipped with special geometric structures, particularly complex and hypercomplex ones. A solvmanifold is the quotient of a simply connected solvable Lie group by a lattice; if the group is nilpotent, the quotient is called a nilmanifold. These manifolds provide important examples in differential geometry—for instance, the Kodaira–Thurston manifold, a compact symplectic non-Kähler manifold, is a nilmanifold.
I study invariant complex and hypercomplex structures that can be analyzed at the Lie algebra level. A key class of Lie algebras in this context is given by the almost abelian ones, which have a codimension-one abelian ideal. Their structure is captured by a single matrix, and its Jordan form helps determine the existence of complex or hypercomplex structures.
There is a strong link between the de Rham cohomology of a solvmanifold and the cohomology of its Lie algebra, especially when the structure matrix has real eigenvalues. In such cases, Hattori’s theorem ensures both cohomologies are isomorphic. When complex eigenvalues are present, computations can sometimes be handled using Kasuya’s methods.
My goal is to compute and understand the cohomology of newly identified complex and hypercomplex almost abelian solvmanifolds.